NASA Astrophysics Data System (ADS)
Lloyd, Seth; Dreyer, Olaf
2016-02-01
Path integrals calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration. This paper defines a universal path integral, which sums over all computable structures. This path integral contains as sub-integrals all possible computable path integrals, including those of field theory, the standard model of elementary particles, discrete models of quantum gravity, string theory, etc. The universal path integral possesses a well-defined measure that guarantees its finiteness. The probabilities for events corresponding to sub-integrals can be calculated using the method of decoherent histories. The universal path integral supports a quantum theory of the universe in which the world that we see around us arises out of the interference between all computable structures.
Path Integrals and Hamiltonians
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.
2014-03-01
1. Synopsis; Part I. Fundamental Principles: 2. The mathematical structure of quantum mechanics; 3. Operators; 4. The Feynman path integral; 5. Hamiltonian mechanics; 6. Path integral quantization; Part II. Stochastic Processes: 7. Stochastic systems; Part III. Discrete Degrees of Freedom: 8. Ising model; 9. Ising model: magnetic field; 10. Fermions; Part IV. Quadratic Path Integrals: 11. Simple harmonic oscillators; 12. Gaussian path integrals; Part V. Action with Acceleration: 13. Acceleration Lagrangian; 14. Pseudo-Hermitian Euclidean Hamiltonian; 15. Non-Hermitian Hamiltonian: Jordan blocks; 16. The quartic potential: instantons; 17. Compact degrees of freedom; Index.
Scattering theory with path integrals
Rosenfelder, R.
2014-03-15
Starting from well-known expressions for the T-matrix and its derivative in standard nonrelativistic potential scattering, I rederive recent path-integral formulations due to Efimov and Barbashov et al. Some new relations follow immediately.
Squeezed states and path integrals
NASA Technical Reports Server (NTRS)
Daubechies, Ingrid; Klauder, John R.
1992-01-01
The continuous-time regularization scheme for defining phase-space path integrals is briefly reviewed as a method to define a quantization procedure that is completely covariant under all smooth canonical coordinate transformations. As an illustration of this method, a limited set of transformations is discussed that have an image in the set of the usual squeezed states. It is noteworthy that even this limited set of transformations offers new possibilities for stationary phase approximations to quantum mechanical propagators.
Perturbative Methods in Path Integration
NASA Astrophysics Data System (ADS)
Johnson-Freyd, Theodore Paul
This dissertation addresses a number of related questions concerning perturbative "path" integrals. Perturbative methods are one of the few successful ways physicists have worked with (or even defined) these infinite-dimensional integrals, and it is important as mathematicians to check that they are correct. Chapter 0 provides a detailed introduction. We take a classical approach to path integrals in Chapter 1. Following standard arguments, we posit a Feynman-diagrammatic description of the asymptotics of the time-evolution operator for the quantum mechanics of a charged particle moving nonrelativistically through a curved manifold under the influence of an external electromagnetic field. We check that our sum of Feynman diagrams has all desired properties: it is coordinate-independent and well-defined without ultraviolet divergences, it satisfies the correct composition law, and it satisfies Schrodinger's equation thought of as a boundary-value problem in PDE. Path integrals in quantum mechanics and elsewhere in quantum field theory are almost always of the shape ∫ f es for some functions f (the "observable") and s (the "action"). In Chapter 2 we step back to analyze integrals of this type more generally. Integration by parts provides algebraic relations between the values of ∫ (-) es for different inputs, which can be packaged into a Batalin--Vilkovisky-type chain complex. Using some simple homological perturbation theory, we study the version of this complex that arises when f and s are taken to be polynomial functions, and power series are banished. We find that in such cases, the entire scheme-theoretic critical locus (complex points included) of s plays an important role, and that one can uniformly (but noncanonically) integrate out in a purely algebraic way the contributions to the integral from all "higher modes," reducing ∫ f es to an integral over the critical locus. This may help explain the presence of analytic continuation in questions like the
Integrated assignment and path planning
NASA Astrophysics Data System (ADS)
Murphey, Robert A.
2005-11-01
A surge of interest in unmanned systems has exposed many new and challenging research problems across many fields of engineering and mathematics. These systems have the potential of transforming our society by replacing dangerous and dirty jobs with networks of moving machines. This vision is fundamentally separate from the modern view of robotics in that sophisticated behavior is realizable not by increasing individual vehicle complexity, but instead through collaborative teaming that relies on collective perception, abstraction, decision making, and manipulation. Obvious examples where collective robotics will make an impact include planetary exploration, space structure assembly, remote and undersea mining, hazardous material handling and clean-up, and search and rescue. Nonetheless, the phenomenon driving this technology trend is the increasing reliance of the US military on unmanned vehicles, specifically, aircraft. Only a few years ago, following years of resistance to the use of unmanned systems, the military and civilian leadership in the United States reversed itself and have recently demonstrated surprisingly broad acceptance of increasingly pervasive use of unmanned platforms in defense surveillance, and even attack. However, as rapidly as unmanned systems have gained acceptance, the defense research community has discovered the technical pitfalls that lie ahead, especially for operating collective groups of unmanned platforms. A great deal of talent and energy has been devoted to solving these technical problems, which tend to fall into two categories: resource allocation of vehicles to objectives, and path planning of vehicle trajectories. An extensive amount of research has been conducted in each direction, yet, surprisingly, very little work has considered the integrated problem of assignment and path planning. This dissertation presents a framework for studying integrated assignment and path planning and then moves on to suggest an exact
Bergman Kernel from Path Integral
NASA Astrophysics Data System (ADS)
Douglas, Michael R.; Klevtsov, Semyon
2010-01-01
We rederive the expansion of the Bergman kernel on Kähler manifolds developed by Tian, Yau, Zelditch, Lu and Catlin, using path integral and perturbation theory, and generalize it to supersymmetric quantum mechanics. One physics interpretation of this result is as an expansion of the projector of wave functions on the lowest Landau level, in the special case that the magnetic field is proportional to the Kähler form. This is relevant for the quantum Hall effect in curved space, and for its higher dimensional generalizations. Other applications include the theory of coherent states, the study of balanced metrics, noncommutative field theory, and a conjecture on metrics in black hole backgrounds discussed in [24]. We give a short overview of these various topics. From a conceptual point of view, this expansion is noteworthy as it is a geometric expansion, somewhat similar to the DeWitt-Seeley-Gilkey et al short time expansion for the heat kernel, but in this case describing the long time limit, without depending on supersymmetry.
White Noise Path Integrals in Stochastic Neurodynamics
NASA Astrophysics Data System (ADS)
Carpio-Bernido, M. Victoria; Bernido, Christopher C.
2008-06-01
The white noise path integral approach is used in stochastic modeling of neural activity, where the primary dynamical variables are the relative membrane potentials, while information on transmembrane ionic currents is contained in the drift coefficient. The white noise path integral allows a natural framework and can be evaluated explicitly to yield a closed form for the conditional probability density.
Path Integral Approach to Atomic Collisions
NASA Astrophysics Data System (ADS)
Harris, Allison
2016-09-01
The Path Integral technique is an alternative formulation of quantum mechanics that is based on a Lagrangian approach. In its exact form, it is completely equivalent to the Hamiltonian-based Schrödinger equation approach. Developed by Feynman in the 1940's, following inspiration from Dirac, the path integral approach has been widely used in high energy physics, quantum field theory, and statistical mechanics. However, only in limited cases has the path integral approach been applied to quantum mechanical few-body scattering. We present a theoretical and computational development of the path integral method for use in the study of atomic collisions. Preliminary results are presented for some simple systems. Ultimately, this approach will be applied to few-body ion-atom collisions. Work supported by NSF grant PHY-1505217.
Local-time representation of path integrals.
Jizba, Petr; Zatloukal, Václav
2015-12-01
We derive a local-time path-integral representation for a generic one-dimensional time-independent system. In particular, we show how to rephrase the matrix elements of the Bloch density matrix as a path integral over x-dependent local-time profiles. The latter quantify the time that the sample paths x(t) in the Feynman path integral spend in the vicinity of an arbitrary point x. Generalization of the local-time representation that includes arbitrary functionals of the local time is also provided. We argue that the results obtained represent a powerful alternative to the traditional Feynman-Kac formula, particularly in the high- and low-temperature regimes. To illustrate this point, we apply our local-time representation to analyze the asymptotic behavior of the Bloch density matrix at low temperatures. Further salient issues, such as connections with the Sturm-Liouville theory and the Rayleigh-Ritz variational principle, are also discussed.
The path integral for dendritic trees.
Abbott, L F; Farhi, E; Gutmann, S
1991-01-01
We construct the path integral for determining the potential on any dendritic tree described by a linear cable equation. This is done by generalizing Brownian motion from a line to a tree. We also construct the path integral for dendritic structures with spatially-varying and/or time-dependent membrane conductivities due, for example, to synaptic inputs. The path integral allows novel computational techniques to be applied to cable problems. Our analysis leads ultimately to an exact expression for the Green's function on a dendritic tree of arbitrary geometry expressed in terms of a set of simple diagrammatic rules. These rules providing a fast and efficient method for solving complex cable problems.
Fermionic path integrals and local anomalies
NASA Astrophysics Data System (ADS)
Roepstorff, G.
2003-05-01
No doubt, the subject of path integrals proved to be an immensely fruitful human, i.e. Feynman's idea. No wonder it is more timely than ever. Some even claim that it is the most daring, innovative and revolutionary idea since the days of Heisenberg and Bohr. It is thus likely to generate enthusiasm, if not addiction among physicists who seek simplicity together with perfection. Professor Devreese's long-lasting interest in, if not passion on the subject stems from his firm conviction that, beyond being the tool of choice, path integration provides the key to all quantum phenomena, be it in solid state, atomic, molecular or particle physics as evidenced by the impressive list of publications at the address http://lib.ua.ac.be/AB/a867.html. In this note, I review a pitfall of fermionic path integrals and a way to get around it in situations relevant to the Standard Model of particle physics.
Optical tomography with discretized path integral
Yuan, Bingzhi; Tamaki, Toru; Kushida, Takahiro; Mukaigawa, Yasuhiro; Kubo, Hiroyuki; Raytchev, Bisser; Kaneda, Kazufumi
2015-01-01
Abstract. We present a framework for optical tomography based on a path integral. Instead of directly solving the radiative transport equations, which have been widely used in optical tomography, we use a path integral that has been developed for rendering participating media based on the volume rendering equation in computer graphics. For a discretized two-dimensional layered grid, we develop an algorithm to estimate the extinction coefficients of each voxel with an interior point method. Numerical simulation results are shown to demonstrate that the proposed method works well. PMID:26839903
Optical tomography with discretized path integral.
Yuan, Bingzhi; Tamaki, Toru; Kushida, Takahiro; Mukaigawa, Yasuhiro; Kubo, Hiroyuki; Raytchev, Bisser; Kaneda, Kazufumi
2015-07-01
We present a framework for optical tomography based on a path integral. Instead of directly solving the radiative transport equations, which have been widely used in optical tomography, we use a path integral that has been developed for rendering participating media based on the volume rendering equation in computer graphics. For a discretized two-dimensional layered grid, we develop an algorithm to estimate the extinction coefficients of each voxel with an interior point method. Numerical simulation results are shown to demonstrate that the proposed method works well.
The formal path integral and quantum mechanics
Johnson-Freyd, Theo
2010-11-15
Given an arbitrary Lagrangian function on R{sup d} and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by 'Feynman diagrams', although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a 'Fubini theorem' expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by 'cutting and pasting' and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic 'formal path integral' for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.
Path integration in tactile perception of shapes.
Moscatelli, Alessandro; Naceri, Abdeldjallil; Ernst, Marc O
2014-11-01
Whenever we move the hand across a surface, tactile signals provide information about the relative velocity between the skin and the surface. If the system were able to integrate the tactile velocity information over time, cutaneous touch may provide an estimate of the relative displacement between the hand and the surface. Here, we asked whether humans are able to form a reliable representation of the motion path from tactile cues only, integrating motion information over time. In order to address this issue, we conducted three experiments using tactile motion and asked participants (1) to estimate the length of a simulated triangle, (2) to reproduce the shape of a simulated triangular path, and (3) to estimate the angle between two-line segments. Participants were able to accurately indicate the length of the path, whereas the perceived direction was affected by a direction bias (inward bias). The response pattern was thus qualitatively similar to the ones reported in classical path integration studies involving locomotion. However, we explain the directional biases as the result of a tactile motion aftereffect.
Bead-Fourier path integral molecular dynamics
NASA Astrophysics Data System (ADS)
Ivanov, Sergei D.; Lyubartsev, Alexander P.; Laaksonen, Aatto
2003-06-01
Molecular dynamics formulation of Bead-Fourier path integral method for simulation of quantum systems at finite temperatures is presented. Within this scheme, both the bead coordinates and Fourier coefficients, defining the path representing the quantum particle, are treated as generalized coordinates with corresponding generalized momenta and masses. Introduction of the Fourier harmonics together with the center-of-mass thermostating scheme is shown to remove the ergodicity problem, known to pose serious difficulties in standard path integral molecular dynamics simulations. The method is tested for quantum harmonic oscillator and hydrogen atom (Coulombic potential). The simulation results are compared with the exact analytical solutions available for both these systems. Convergence of the results with respect to the number of beads and Fourier harmonics is analyzed. It was shown that addition of a few Fourier harmonics already improves the simulation results substantially, even for a relatively small number of beads. The proposed Bead-Fourier path integral molecular dynamics is a reliable and efficient alternative to simulations of quantum systems.
A taxonomy of integral reaction path analysis
Grcar, Joseph F.; Day, Marcus S.; Bell, John B.
2004-12-23
W. C. Gardiner observed that achieving understanding through combustion modeling is limited by the ability to recognize the implications of what has been computed and to draw conclusions about the elementary steps underlying the reaction mechanism. This difficulty can be overcome in part by making better use of reaction path analysis in the context of multidimensional flame simulations. Following a survey of current practice, an integral reaction flux is formulated in terms of conserved scalars that can be calculated in a fully automated way. Conditional analyses are then introduced, and a taxonomy for bidirectional path analysis is explored. Many examples illustrate the resulting path analysis and uncover some new results about nonpremixed methane-air laminar jets.
Path-integral approach to lattice polarons
NASA Astrophysics Data System (ADS)
Kornilovitch, P. E.
2007-06-01
The basic principles behind a path integral approach to the lattice polaron are reviewed. Analytical integration of phonons reduces the problem to one self-interacting imaginary-time path, which is then simulated by Metropolis Monte Carlo. Projection operators separate states of different symmetry, which provides access to various excited states. Shifted boundary conditions in imaginary time enable calculation of the polaron mass, spectrum and density of states. Other polaron characteristics accessible by the method include the polaron energy, number of excited phonons and isotope exponent on mass. Monte Carlo updates are formulated in continuous imaginary time on infinite lattices and as such provide statistically unbiased results without finite-size and finite time-step errors. Numerical data are presented for models with short-range and long-range electron-phonon interactions.
An alternative path integral for quantum gravity
NASA Astrophysics Data System (ADS)
Krishnan, Chethan; Kumar, K. V. Pavan; Raju, Avinash
2016-10-01
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in D dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This "Neumann ensemble" perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.
Quantitative molecular thermochemistry based on path integrals.
Glaesemann, Kurt R; Fried, Laurence E
2005-07-15
The calculation of thermochemical data requires accurate molecular energies and heat capacities. Traditional methods rely upon the standard harmonic normal-mode analysis to calculate the vibrational and rotational contributions. We utilize path-integral Monte Carlo for going beyond the harmonic analysis and to calculate the vibrational and rotational contributions to ab initio energies. This is an application and an extension of a method previously developed in our group [J. Chem. Phys. 118, 1596 (2003)].
Path integration: effect of curved path complexity and sensory system on blindfolded walking.
Koutakis, Panagiotis; Mukherjee, Mukul; Vallabhajosula, Srikant; Blanke, Daniel J; Stergiou, Nicholas
2013-02-01
Path integration refers to the ability to integrate continuous information of the direction and distance traveled by the system relative to the origin. Previous studies have investigated path integration through blindfolded walking along simple paths such as straight line and triangles. However, limited knowledge exists regarding the role of path complexity in path integration. Moreover, little is known about how information from different sensory input systems (like vision and proprioception) contributes to accurate path integration. The purpose of the current study was to investigate how sensory information and curved path complexity affect path integration. Forty blindfolded participants had to accurately reproduce a curved path and return to the origin. They were divided into four groups that differed in the curved path, circle (simple) or figure-eight (complex), and received either visual (previously seen) or proprioceptive (previously guided) information about the path before they reproduced it. The dependent variables used were average trajectory error, walking speed, and distance traveled. The results indicated that (a) both groups that walked on a circular path and both groups that received visual information produced greater accuracy in reproducing the path. Moreover, the performance of the group that received proprioceptive information and later walked on a figure-eight path was less accurate than their corresponding circular group. The groups that had the visual information also walked faster compared to the group that had proprioceptive information. Results of the current study highlight the roles of different sensory inputs while performing blindfolded walking for path integration.
Path integration in desert ants, Cataglyphis fortis
Müller, Martin; Wehner, Rüdiger
1988-01-01
Foraging desert ants, Cataglyphis fortis, continually keep track of their own posotions relative to home— i.e., integrate their tortuous outbound routes and return home along straight (inbound) routes. By experimentally manipulating the ants' outbound trajectories we show that the ants solve this path integration problem not by performing a true vector summation (as a human navigator does) but by employing a computationally simple approximation. This approximation is characterized by small, but systematic, navigational errors that helped us elucidate the ant's way of computing its mean home vector. PMID:16593958
Path integral quantization of generalized quantum electrodynamics
Bufalo, R.; Pimentel, B. M.; Zambrano, G. E. R.
2011-02-15
In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the Hamiltonian structure of the system following Dirac's methodology and, then, we followed the Faddeev-Senjanovic procedure to obtain the transition amplitude. The complete propagators (Schwinger-Dyson-Fradkin equations) of the correct gauge fixation and the generalized Ward-Fradkin-Takahashi identities are also obtained. Afterwards, an explicit calculation of one-loop approximations of all Green's functions and a discussion about the obtained results are presented.
High order path integrals made easy
NASA Astrophysics Data System (ADS)
Kapil, Venkat; Behler, Jörg; Ceriotti, Michele
2016-12-01
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the system. Many approaches have been suggested to reduce the required number of replicas. Among these, high-order factorizations of the Boltzmann operator are particularly attractive for high-precision and low-temperature scenarios. Unfortunately, to date, several technical challenges have prevented a widespread use of these approaches to study the nuclear quantum effects in condensed-phase systems. Here we introduce an inexpensive molecular dynamics scheme that overcomes these limitations, thus making it possible to exploit the improved convergence of high-order path integrals without having to sacrifice the stability, convenience, and flexibility of conventional second-order techniques. The capabilities of the method are demonstrated by simulations of liquid water and ice, as described by a neural-network potential fitted to the dispersion-corrected hybrid density functional theory calculations.
Building a cognitive map by assembling multiple path integration systems.
Wang, Ranxiao Frances
2016-06-01
Path integration and cognitive mapping are two of the most important mechanisms for navigation. Path integration is a primitive navigation system which computes a homing vector based on an animal's self-motion estimation, while cognitive map is an advanced spatial representation containing richer spatial information about the environment that is persistent and can be used to guide flexible navigation to multiple locations. Most theories of navigation conceptualize them as two distinctive, independent mechanisms, although the path integration system may provide useful information for the integration of cognitive maps. This paper demonstrates a fundamentally different scenario, where a cognitive map is constructed in three simple steps by assembling multiple path integrators and extending their basic features. The fact that a collection of path integration systems can be turned into a cognitive map suggests the possibility that cognitive maps may have evolved directly from the path integration system.
Path Integral Monte Carlo Methods for Fermions
NASA Astrophysics Data System (ADS)
Ethan, Ethan; Dubois, Jonathan; Ceperley, David
2014-03-01
In general, Quantum Monte Carlo methods suffer from a sign problem when simulating fermionic systems. This causes the efficiency of a simulation to decrease exponentially with the number of particles and inverse temperature. To circumvent this issue, a nodal constraint is often implemented, restricting the Monte Carlo procedure from sampling paths that cause the many-body density matrix to change sign. Unfortunately, this high-dimensional nodal surface is not a priori known unless the system is exactly solvable, resulting in uncontrolled errors. We will discuss two possible routes to extend the applicability of finite-temperatue path integral Monte Carlo. First we extend the regime where signful simulations are possible through a novel permutation sampling scheme. Afterwards, we discuss a method to variationally improve the nodal surface by minimizing a free energy during simulation. Applications of these methods will include both free and interacting electron gases, concluding with discussion concerning extension to inhomogeneous systems. Support from DOE DE-FG52-09NA29456, DE-AC52-07NA27344, LLNL LDRD 10- ERD-058, and the Lawrence Scholar program.
The path integral picture of quantum systems
NASA Astrophysics Data System (ADS)
Ceperley, David
2011-03-01
The imaginary time path integral ``formalism'' was introduced in 1953 by Feynman to understand the superfluid transition in liquid helium. The equilibrium properties of quantum many body systems is isomorphic to the classical statistical mechanics of cross-linking polymer-like objects. With the Markov Chain Monte Carlo method, invented by Metropolis et al., also in 1953, a potential way of calculating properties of correlated quantum systems was in place. But calculations for many-body quantum systems did not become routine until computers and algorithms had become sufficiently powerful three decades later. Once such simulations could happen, it was realized that simulations provided a deeper insight into boson superfluids, in particular the relation of bose condensation to the polymer end-to-end distance, and the superfluid density to the polymer ``winding number.'' Some recent developments and applications to supersolids, and helium droplets will be given. Finally, limitations of the methodology e.g. to fermion systems are discussed.
Polymer quantum mechanics some examples using path integrals
Parra, Lorena; Vergara, J. David
2014-01-14
In this work we analyze several physical systems in the context of polymer quantum mechanics using path integrals. First we introduce the group averaging method to quantize constrained systems with path integrals and later we use this procedure to compute the effective actions for the polymer non-relativistic particle and the polymer harmonic oscillator. We analyze the measure of the path integral and we describe the semiclassical dynamics of the systems.
Mixed time slicing in path integral simulations
NASA Astrophysics Data System (ADS)
Steele, Ryan P.; Zwickl, Jill; Shushkov, Philip; Tully, John C.
2011-02-01
A simple and efficient scheme is presented for using different time slices for different degrees of freedom in path integral calculations. This method bridges the gap between full quantization and the standard mixed quantum-classical (MQC) scheme and, therefore, still provides quantum mechanical effects in the less-quantized variables. Underlying the algorithm is the notion that time slices (beads) may be "collapsed" in a manner that preserves quantization in the less quantum mechanical degrees of freedom. The method is shown to be analogous to multiple-time step integration techniques in classical molecular dynamics. The algorithm and its associated error are demonstrated on model systems containing coupled high- and low-frequency modes; results indicate that convergence of quantum mechanical observables can be achieved with disparate bead numbers in the different modes. Cost estimates indicate that this procedure, much like the MQC method, is most efficient for only a relatively few quantum mechanical degrees of freedom, such as proton transfer. In this regime, however, the cost of a fully quantum mechanical simulation is determined by the quantization of the least quantum mechanical degrees of freedom.
Path-Integral Derivation of Lifshitz Tails
NASA Astrophysics Data System (ADS)
Sa-Yakanit, V.
2008-11-01
The behavior of the electron density of states (DOS) for the Lifshitz tail states is studied in the limit of low energy using the Feynman path-integral method. This method was used to study the heavily doped semiconductors for the case of a Gaussian random potential. The main results obtained are that the tail states behave as DOS exp (-B(E)), with B(E) = En, n = {1 / 2} for short-range interaction and n = 2 for long-range interaction. In this study it is shown that without the Gaussian approximation, the behavior of the Lifshitz tails for the Poisson distribution is obtained as DOS exp (-B(E)) with B(E) = En, n = {3 / 2} . As in the case of heavily doped semiconductor, the method can be easily generalized to long-range interactions. A comparison with the method developed by Friedberg and Luttinger based on the reformulation of the problem in terms of Brownian motion is given.
Differential neural network configuration during human path integration.
Arnold, Aiden E G F; Burles, Ford; Bray, Signe; Levy, Richard M; Iaria, Giuseppe
2014-01-01
Path integration is a fundamental skill for navigation in both humans and animals. Despite recent advances in unraveling the neural basis of path integration in animal models, relatively little is known about how path integration operates at a neural level in humans. Previous attempts to characterize the neural mechanisms used by humans to visually path integrate have suggested a central role of the hippocampus in allowing accurate performance, broadly resembling results from animal data. However, in recent years both the central role of the hippocampus and the perspective that animals and humans share similar neural mechanisms for path integration has come into question. The present study uses a data driven analysis to investigate the neural systems engaged during visual path integration in humans, allowing for an unbiased estimate of neural activity across the entire brain. Our results suggest that humans employ common task control, attention and spatial working memory systems across a frontoparietal network during path integration. However, individuals differed in how these systems are configured into functional networks. High performing individuals were found to more broadly express spatial working memory systems in prefrontal cortex, while low performing individuals engaged an allocentric memory system based primarily in the medial occipito-temporal region. These findings suggest that visual path integration in humans over short distances can operate through a spatial working memory system engaging primarily the prefrontal cortex and that the differential configuration of memory systems recruited by task control networks may help explain individual biases in spatial learning strategies.
Path integrals and the WKB approximation in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay; Campiglia, Miguel; Henderson, Adam
2010-12-01
We follow the Feynman procedure to obtain a path integral formulation of loop quantum cosmology starting from the Hilbert space framework. Quantum geometry effects modify the weight associated with each path so that the effective measure on the space of paths is different from that used in the Wheeler-DeWitt theory. These differences introduce some conceptual subtleties in arriving at the WKB approximation. But the approximation is well defined and provides intuition for the differences between loop quantum cosmology and the Wheeler-DeWitt theory from a path integral perspective.
Two-path plasmonic interferometer with integrated detector
Dyer, Gregory Conrad; Shaner, Eric A.; Aizin, Gregory
2016-03-29
An electrically tunable terahertz two-path plasmonic interferometer with an integrated detection element can down convert a terahertz field to a rectified DC signal. The integrated detector utilizes a resonant plasmonic homodyne mixing mechanism that measures the component of the plasma waves in-phase with an excitation field that functions as the local oscillator in the mixer. The plasmonic interferometer comprises two independently tuned electrical paths. The plasmonic interferometer enables a spectrometer-on-a-chip where the tuning of electrical path length plays an analogous role to that of physical path length in macroscopic Fourier transform interferometers.
Selecta from a Life-Long Obsession with Path Integrals
Klauder, John R.
2008-06-18
The definition and interpretation of canonical, phase space path integrals has evolved over many years to achieve a form that now admits a correct and rigorous formulation, which is also covariant under canonical coordinate transformations. Such formulations involve coherent state representations, which, in their modern version, were originally introduced as an alternative tool to construct phase space path integrals. Moreover, coherent state representations lead to physical interpretations that are more natural than those afforded by more traditional representations. Suitable continuous time regularization procedures lead to a covariant phase space path integral formulation that greatly clarifies the vague phrase that canonical quantization requires Cartesian coordinates.
The application of path integral for log return probability calculation
NASA Astrophysics Data System (ADS)
Palupi, D. S.; Hermanto, A.; Tenderlilin, E.; Rosyid, M. F.
2014-10-01
Log return probability has been calculated using path integral method. The stock price is assumed obeying the stochastic differential equation of a geometric Brownian motion and the volatility is assumed following Ornstein Uhlenbeck process. The stochastic differential equation of stock price and volatility lead to Fokker-Plank equation. The Fokker-Plank equation is solved using path integral method. Distribution of log return can be used to take the valuation ln return stock.
Variational path integral molecular dynamics study of a water molecule
NASA Astrophysics Data System (ADS)
Miura, Shinichi
2013-08-01
In the present study, a variational path integral molecular dynamics method developed by the author [Chem. Phys. Lett. 482, 165 (2009)] is applied to a water molecule on the adiabatic potential energy surface. The method numerically generates an exact wavefunction using a trial wavefunction of the target system. It has been shown that even if a poor trial wavefunction is employed, the exact quantum distribution is numerically extracted, demonstrating the robustness of the variational path integral method.
Sensory feedback in a bump attractor model of path integration.
Poll, Daniel B; Nguyen, Khanh; Kilpatrick, Zachary P
2016-04-01
Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal's current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal's knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541-4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error.
Characterizing regulatory path motifs in integrated networks using perturbational data
2010-01-01
We introduce Pathicular http://bioinformatics.psb.ugent.be/software/details/Pathicular, a Cytoscape plugin for studying the cellular response to perturbations of transcription factors by integrating perturbational expression data with transcriptional, protein-protein and phosphorylation networks. Pathicular searches for 'regulatory path motifs', short paths in the integrated physical networks which occur significantly more often than expected between transcription factors and their targets in the perturbational data. A case study in Saccharomyces cerevisiae identifies eight regulatory path motifs and demonstrates their biological significance. PMID:20230615
Path Integrals and Exotic Options:. Methods and Numerical Results
NASA Astrophysics Data System (ADS)
Bormetti, G.; Montagna, G.; Moreni, N.; Nicrosini, O.
2005-09-01
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price path dependent options on multidimensional and correlated underlying assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the case of Asian call options. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at the money (ATM) and out of the money (OTM) options, path integral exhibits competitive performances.
The perturbative approach to path integrals: A succinct mathematical treatment
NASA Astrophysics Data System (ADS)
Nguyen, Timothy
2016-09-01
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows one to evaluate integrals perturbatively, i.e., as a series expansion in a formal parameter irrespective of convergence properties. We establish invariance properties of such a Wick expansion under coordinate changes and the action of a Lie group of symmetries, and we use this to study essential features of path integral manipulations, including coordinate changes, Ward identities, Schwinger-Dyson equations, Faddeev-Popov gauge-fixing, and eliminating fields by their equation of motion. We also discuss the asymptotic nature of the Wick expansion and the implications this has for defining path integrals perturbatively and nonperturbatively.
Medial temporal lobe roles in human path integration.
Yamamoto, Naohide; Philbeck, John W; Woods, Adam J; Gajewski, Daniel A; Arthur, Joeanna C; Potolicchio, Samuel J; Levy, Lucien; Caputy, Anthony J
2014-01-01
Path integration is a process in which observers derive their location by integrating self-motion signals along their locomotion trajectory. Although the medial temporal lobe (MTL) is thought to take part in path integration, the scope of its role for path integration remains unclear. To address this issue, we administered a variety of tasks involving path integration and other related processes to a group of neurosurgical patients whose MTL was unilaterally resected as therapy for epilepsy. These patients were unimpaired relative to neurologically intact controls in many tasks that required integration of various kinds of sensory self-motion information. However, the same patients (especially those who had lesions in the right hemisphere) walked farther than the controls when attempting to walk without vision to a previewed target. Importantly, this task was unique in our test battery in that it allowed participants to form a mental representation of the target location and anticipate their upcoming walking trajectory before they began moving. Thus, these results put forth a new idea that the role of MTL structures for human path integration may stem from their participation in predicting the consequences of one's locomotor actions. The strengths of this new theoretical viewpoint are discussed.
Low level constraints on dynamic contour path integration.
Hall, Sophie; Bourke, Patrick; Guo, Kun
2014-01-01
Contour integration is a fundamental visual process. The constraints on integrating discrete contour elements and the associated neural mechanisms have typically been investigated using static contour paths. However, in our dynamic natural environment objects and scenes vary over space and time. With the aim of investigating the parameters affecting spatiotemporal contour path integration, we measured human contrast detection performance of a briefly presented foveal target embedded in dynamic collinear stimulus sequences (comprising five short 'predictor' bars appearing consecutively towards the fovea, followed by the 'target' bar) in four experiments. The data showed that participants' target detection performance was relatively unchanged when individual contour elements were separated by up to 2° spatial gap or 200 ms temporal gap. Randomising the luminance contrast or colour of the predictors, on the other hand, had similar detrimental effect on grouping dynamic contour path and subsequent target detection performance. Randomising the orientation of the predictors reduced target detection performance greater than introducing misalignment relative to the contour path. The results suggest that the visual system integrates dynamic path elements to bias target detection even when the continuity of path is disrupted in terms of spatial (2°), temporal (200 ms), colour (over 10 colours) and luminance (-25% to 25%) information. We discuss how the findings can be largely reconciled within the functioning of V1 horizontal connections.
Canonical formulation and path integral for local vacuum energy sequestering
NASA Astrophysics Data System (ADS)
Bufalo, R.; KlusoÅ, J.; Oksanen, M.
2016-08-01
We establish the Hamiltonian analysis and the canonical path integral for a local formulation of vacuum energy sequestering. In particular, by considering the state of the Universe as a superposition of vacuum states corresponding to different values of the cosmological and gravitational constants, the path integral is extended to include integrations over the cosmological and gravitational constants. The result is an extension of the Ng-van Dam form of the path integral of unimodular gravity. It is argued to imply a relation between the fraction of the most likely values of the gravitational and cosmological constants and the average values of the energy density and pressure of matter over spacetime. Finally, we construct and analyze a Becchi-Rouet-Stora-Tyutin-exact formulation of the theory, which can be considered as a topological field theory.
Mielke, Steven L; Truhlar, Donald G
2016-01-21
Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. We now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. We also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function.
Linearized path integral approach for calculating nonadiabatic time correlation functions.
Bonella, Sara; Montemayor, Daniel; Coker, David F
2005-05-10
We show that quantum time correlation functions including electronically nonadiabatic effects can be computed by using an approach in which their path integral expression is linearized in the difference between forward and backward nuclear paths while the electronic component of the amplitude, represented in the mapping formulation, can be computed exactly, leading to classical-like equations of motion for all degrees of freedom. The efficiency of this approach is demonstrated in some simple model applications.
Integrated Schools: Finding a New Path
ERIC Educational Resources Information Center
Orfield, Gary; Frankenberg, Erica; Siegel-Hawley, Genevieve
2010-01-01
Research shows that schools remain a powerful tool for shoring up individual opportunity and for attaining a thriving, multiracial democratic society. The authors point to social science evidence that demonstrates how segregated schooling limits the prospects of both minority and majority students and how integrated education can close the…
Faddeev-Jackiw quantization and the path integral
NASA Astrophysics Data System (ADS)
Toms, David J.
2015-11-01
The method for quantization of constrained theories that was suggested originally by Faddeev and Jackiw along with later modifications is discussed. The particular emphasis of this paper is to show how it is simple to implement their method within the path integral framework using the natural geometric structure that their method utilizes. The procedure is exemplified with the analysis of two models: a quantum mechanical particle constrained to a surface (of which the hypersphere is a special case), and a quantized Schrödinger field interacting with a quantized vector field for both the massive and the massless cases. The results are shown to agree with what is found using the Dirac method for constrained path integrals. We comment on a previous path integral analysis of the Faddeev-Jackiw method. We also discuss why a previous criticism of the Faddeev-Jackiw method is unfounded and why suggested modifications of their method are unnecessary.
Master equations and the theory of stochastic path integrals.
Weber, Markus F; Frey, Erwin
2017-04-01
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon
Master equations and the theory of stochastic path integrals
NASA Astrophysics Data System (ADS)
Weber, Markus F.; Frey, Erwin
2017-04-01
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers–Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman–Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a ‘generating functional’, which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a ‘forward’ and a ‘backward’ path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered
Predator-prey quasicycles from a path-integral formalism.
Butler, Thomas; Reynolds, David
2009-03-01
The existence of beyond mean-field quasicycle oscillations in a simple spatial model of predator-prey interactions is derived from a path-integral formalism. The results agree substantially with those obtained from analysis of similar models using system size expansions of the master equation. In all of these analyses, the discrete nature of predator-prey populations and finite-size effects lead to persistent oscillations in time, but spatial patterns fail to form. The path-integral formalism goes beyond mean-field theory and provides a focus on individual realizations of the stochastic time evolution of population not captured in the standard master-equation approach.
Action with Acceleration i: Euclidean Hamiltonian and Path Integral
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.
2013-10-01
An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and velocity — and hence the Euclidean Hamiltonian depends on two degrees of freedom. The Hamiltonian for the acceleration system is non-Hermitian and can be mapped to a Hermitian Hamiltonian using a similarity transformation; the matrix elements of the similarity transformation are explicitly evaluated.
Path Integrals and the Statistical Thermodynamics of Black Holes.
NASA Astrophysics Data System (ADS)
Martinez, Erik Andres
The path integral is an important element in modern approaches to the quantization of the gravitational field. Path integral representations of partition functions for static and stationary black hole systems as well as path integrals for minisuperspace models of cosmology are presented. The functional integral is defined throughout as a sum over Lorentzian histories. A consistent formulation of Feynman's prescription to construct partition functions in terms of path integrals for general gravitational systems is presented and contrasted with other "Euclideanization" prescriptions. It is shown that the central object in the description of black hole systems is the gravitational action. In particular, the additivity of the entropies of matter and black holes in thermal equilibrium is a consequence of the additivity of their corresponding actions, and thermodynamic potentials like the energy or the pressure are not in general addivite when gravity plays an important role. Partition functions as stationary phase approximations of functional integrals for all the thermodynamic ensembles are then constructed by including gravitation as a part of the thermodynamical system. We show that a complex geometry is required to derive the thermodynamic properties of stationary geometries from the sum over histories. The corresponding real "thermodynamical" action is calculated explicitly and the thermodynamical data that imply thermal equilibrium in the presence of a rotating black hole in interaction with matter fields are presented and related to geometrical data. Some of the consequences for Kerr-Newman black hole systems are also discussed. For minisuperspace cosmologies the Lorentzian path integral is a Green function for the Wheeler-DeWitt operator, and its real part is a solution to the Wheeler -DeWitt equation. It is computed explicitly for the de Sitter minisuperspace model. The resulting Green function is then related to both the Hartle-Hawking and tunneling wave
Transport path optimization algorithm based on fuzzy integrated weights
NASA Astrophysics Data System (ADS)
Hou, Yuan-Da; Xu, Xiao-Hao
2014-11-01
Natural disasters cause significant damage to roads, making route selection a complicated logistical problem. To overcome this complexity, we present a method of using a trapezoidal fuzzy number to select the optimal transport path. Using the given trapezoidal fuzzy edge coefficients, we calculate a fuzzy integrated matrix, and incorporate the fuzzy multi-weights into fuzzy integrated weights. The optimal path is determined by taking two sets of vertices and transforming undiscovered vertices into discoverable ones. Our experimental results show that the model is highly accurate, and requires only a few measurement data to confirm the optimal path. The model provides an effective, feasible, and convenient method to obtain weights for different road sections, and can be applied to road planning in intelligent transportation systems.
The Path Integral Formulation of Climate Dynamics
Navarra, Antonio; Tribbia, Joe; Conti, Giovanni
2013-01-01
The chaotic nature of the atmospheric dynamics has stimulated the applications of methods and ideas derived from statistical dynamics. For instance, ensemble systems are used to make weather predictions recently extensive, which are designed to sample the phase space around the initial condition. Such an approach has been shown to improve substantially the usefulness of the forecasts since it allows forecasters to issue probabilistic forecasts. These works have modified the dominant paradigm of the interpretation of the evolution of atmospheric flows (and oceanic motions to some extent) attributing more importance to the probability distribution of the variables of interest rather than to a single representation. The ensemble experiments can be considered as crude attempts to estimate the evolution of the probability distribution of the climate variables, which turn out to be the only physical quantity relevant to practice. However, little work has been done on a direct modeling of the probability evolution itself. In this paper it is shown that it is possible to write the evolution of the probability distribution as a functional integral of the same kind introduced by Feynman in quantum mechanics, using some of the methods and results developed in statistical physics. The approach allows obtaining a formal solution to the Fokker-Planck equation corresponding to the Langevin-like equation of motion with noise. The method is very general and provides a framework generalizable to red noise, as well as to delaying differential equations, and even field equations, i.e., partial differential equations with noise, for example, general circulation models with noise. These concepts will be applied to an example taken from a simple ENSO model. PMID:23840577
Path Integral for Dirac oscillator with generalized uncertainty principle
Benzair, H.; Boudjedaa, T.; Merad, M.
2012-12-15
The propagator for Dirac oscillator in (1+1) dimension, with deformed commutation relation of the Heisenberg principle, is calculated using path integral in quadri-momentum representation. As the mass is related to momentum, we then adapt the space-time transformation method to evaluate quantum corrections and this latter is dependent from the point discretization interval.
Quantum tunneling splittings from path-integral molecular dynamics
NASA Astrophysics Data System (ADS)
Mátyus, Edit; Wales, David J.; Althorpe, Stuart C.
2016-03-01
We illustrate how path-integral molecular dynamics can be used to calculate ground-state tunnelling splittings in molecules or clusters. The method obtains the splittings from ratios of density matrix elements between the degenerate wells connected by the tunnelling. We propose a simple thermodynamic integration scheme for evaluating these elements. Numerical tests on fully dimensional malonaldehyde yield tunnelling splittings in good overall agreement with the results of diffusion Monte Carlo calculations.
What is the right time for path integrals?
NASA Astrophysics Data System (ADS)
Jones, Eric; Bach, Roger; Batelaan, Herman
2013-05-01
The Feynman path integral formulation of quantum mechanics has proven to be a powerful tool for calculations in matter optics. It is natural to introduce the path integral in the context of Young's double slit experiment for matter waves as Feynman did, perhaps after discussing the analogous situation for optics. While intuitive, this approach can lead to a pedagogical misrepresentation of the theory, namely in the phase accumulated along single free-particle trajectories. How is the use of the accumulated phase, 2 πL /λdB , along a path of length L justified? The free-particle action gives a phase that differs by a factor of two. The guiding principle that interference occurs only for two paths that are indistinguishable from one another provides a correct solution: interfering paths must originate and terminate at equal times. We will present several simple thought experiments to illustrate incorrect and correct methods for determining phase shifts. We gratefully acknowledge support from NSF and the DoE GAANN. We thank Ron Cappelletti for interesting discussions.
Path integrals and large deviations in stochastic hybrid systems
NASA Astrophysics Data System (ADS)
Bressloff, Paul C.; Newby, Jay M.
2014-04-01
We construct a path-integral representation of solutions to a stochastic hybrid system, consisting of one or more continuous variables evolving according to a piecewise-deterministic dynamics. The differential equations for the continuous variables are coupled to a set of discrete variables that satisfy a continuous-time Markov process, which means that the differential equations are only valid between jumps in the discrete variables. Examples of stochastic hybrid systems arise in biophysical models of stochastic ion channels, motor-driven intracellular transport, gene networks, and stochastic neural networks. We use the path-integral representation to derive a large deviation action principle for a stochastic hybrid system. Minimizing the associated action functional with respect to the set of all trajectories emanating from a metastable state (assuming that such a minimization scheme exists) then determines the most probable paths of escape. Moreover, evaluating the action functional along a most probable path generates the so-called quasipotential used in the calculation of mean first passage times. We illustrate the theory by considering the optimal paths of escape from a metastable state in a bistable neural network.
Free energies from integral equation theories: enforcing path independence.
Kast, Stefan M
2003-04-01
A variational formalism is constructed for deriving the chemical potential and the Helmholtz free energy in various statistical-mechanical integral equation theories of fluids. Nonzero bridge functions extending the scope of the theories beyond the hypernetted chain approximation can be classified as to whether or not they imply path dependence of the free energy. Classes of bridge functions free of the path dependence problem are derived, based on which a route is devised toward direct computation of free energies from the simulation of a single state.
Tackling higher derivative ghosts with the Euclidean path integral
Fontanini, Michele; Trodden, Mark
2011-05-15
An alternative to the effective field theory approach to treat ghosts in higher derivative theories is to attempt to integrate them out via the Euclidean path integral formalism. It has been suggested that this method could provide a consistent framework within which we might tolerate the ghost degrees of freedom that plague, among other theories, the higher derivative gravity models that have been proposed to explain cosmic acceleration. We consider the extension of this idea to treating a class of terms with order six derivatives, and find that for a general term the Euclidean path integral approach works in the most trivial background, Minkowski. Moreover we see that even in de Sitter background, despite some difficulties, it is possible to define a probability distribution for tensorial perturbations of the metric.
NASA Astrophysics Data System (ADS)
Kleinert, H.; Chervyakov, A.
2000-03-01
We show how to perform integrals over products of distributions in coordinate space such as to reproduce the results of momentum space Feynman integrals in dimensional regularization. This ensures the invariance of path integrals under coordinate transformations. The integrals are performed by expressing the propagators in /1-ɛ dimensions in terms of modified Bessel functions.
BOOK REVIEW: Path Integrals in Field Theory: An Introduction
NASA Astrophysics Data System (ADS)
Ryder, Lewis
2004-06-01
In the 1960s Feynman was known to particle physicists as one of the people who solved the major problems of quantum electrodynamics, his contribution famously introducing what are now called Feynman diagrams. To other physicists he gained a reputation as the author of the Feynman Lectures on Physics; in addition some people were aware of his work on the path integral formulation of quantum theory, and a very few knew about his work on gravitation and Yang--Mills theories, which made use of path integral methods. Forty years later the scene is rather different. Many of the problems of high energy physics are solved; and the standard model incorporates Feynman's path integral method as a way of proving the renormalisability of the gauge (Yang--Mills) theories involved. Gravitation is proving a much harder nut to crack, but here also questions of renormalisability are couched in path-integral language. What is more, theoretical studies of condensed matter physics now also appeal to this technique for quantisation, so the path integral method is becoming part of the standard apparatus of theoretical physics. Chapters on it appear in a number of recent books, and a few books have appeared devoted to this topic alone; the book under review is a very recent one. Path integral techniques have the advantage of enormous conceptual appeal and the great disadvantage of mathematical complexity, this being partly the result of messy integrals but more fundamentally due to the notions of functional differentiation and integration which are involved in the method. All in all this subject is not such an easy ride. Mosel's book, described as an introduction, is aimed at graduate students and research workers in particle physics. It assumes a background knowledge of quantum mechanics, both non-relativistic and relativistic. After three chapters on the path integral formulation of non-relativistic quantum mechanics there are eight chapters on scalar and spinor field theory, followed
Path integration and perturbation theory with complex Euclidean actions
Alexanian, Garnik; MacKenzie, R.; Paranjape, M. B.; Ruel, Jonathan
2008-05-15
The Euclidean path integral quite often involves an action that is not completely real, i.e. a complex action. This occurs when the Minkowski action contains t-odd CP-violating terms. This usually consists of topological terms, such as the Chern-Simons term in odd dimensions, the Wess-Zumino term, the {theta} term or Chern character in 4-dimensional gauge theories, or other topological densities. Analytic continuation to Euclidean time yields an imaginary term in the Euclidean action. It also occurs when the action contains fermions, the fermion path integral being in general a sum over positive and negative real numbers. Negative numbers correspond to the exponential of i{pi} and hence indicate the presence of an imaginary term in the action. In the presence of imaginary terms in the Euclidean action, the usual method of perturbative quantization can fail. Here the action is expanded about its critical points, the quadratic part serving to define the Gaussian free theory and the higher order terms defining the perturbative interactions. For a complex action, the critical points are generically obtained at complex field configurations. Hence the contour of path integration does not pass through the critical points and the perturbative paradigm cannot be directly implemented. The contour of path integration has to be deformed to pass through the complex critical point using a generalized method of steepest descent, in order to do so. Typically, this procedure is not followed. Rather, only the real part of the Euclidean action is considered, and its critical points are used to define the perturbation theory, a procedure that can lead to incorrect results. In this article we present a simple example to illustrate this point. The example consists of N scalar fields in 0+1 dimensions interacting with a U(1) gauge field in the presence of a Chern-Simons term. In this example the path integral can be done exactly, the procedure of deformation of the contour of path
A path integral approach to age dependent branching processes
NASA Astrophysics Data System (ADS)
Greenman, Chris D.
2017-03-01
Age dependent population dynamics are frequently modeled with generalizations of the classic McKendrick–von Foerster equation. These are deterministic systems, and a stochastic generalization was recently reported in Greenman and Chou (2016 Phys. Rev. E 93 012112, 2016 J. Stat. Phys. 16449). Here we develop a fully stochastic theory for age-structured populations via quantum field theoretical Doi–Peliti techniques. This results in a path integral formulation where birth and death events correspond to cubic and quadratic interaction terms. This formalism allows us to efficiently recapitulate the results in Greenman and Chou (2016 Phys. Rev. E 93 012112, 2016 J. Stat. Phys. 16449), exemplifying the utility of Doi–Peliti methods. Furthermore, we find that the path integral formulation for age-structured moments has an exact perturbative expansion that explicitly relates to the hereditary structure between correlated individuals. These methods are then generalized with a binary fission model of cell division.
Three dimensional path integration in the house mouse (Mus domestica)
NASA Astrophysics Data System (ADS)
Bardunias, Paul M.; Jander, R.
Previous studies have explored two-dimensional path integration in rodents by recording responses to passive rotation on a horizontal plane. This study adds the element of passive rotation in a vertical plane, necessitating the mouse to integrate positional information from three dimensions. Mice were trained to climb a wire mesh joining two horizontal planes. The whole arena was rotated 90° while the mouse was vertically oriented as it moved between planes. Rotation was conducted both clockwise and counter-clockwise, controls being provided by rotation of the arena while the mouse was in its nest-box. All 16 mice tested altered their direction of travel subsequent to rotation in the vertical plane, compensating with a change in their path on the following horizontal plane.
Spin foam models for quantum gravity from lattice path integrals
Bonzom, Valentin
2009-09-15
Spin foam models for quantum gravity are derived from lattice path integrals. The setting involves variables from both lattice BF theory and Regge calculus. The action consists in a Regge action, which depends on areas, dihedral angles and includes the Immirzi parameter. In addition, a measure is inserted to ensure a consistent gluing of simplices, so that the amplitude is dominated by configurations that satisfy the parallel transport relations. We explicitly compute the path integral as a sum over spin foams for a generic measure. The Freidel-Krasnov and Engle-Pereira-Rovelli models correspond to a special choice of gluing. In this case, the equations of motion describe genuine geometries, where the constraints of area-angle Regge calculus are satisfied. Furthermore, the Immirzi parameter drops out of the on-shell action, and stationarity with respect to area variations requires spacetime geometry to be flat.
Three dimensional path integration in the house mouse (Mus domestica).
Bardunias, P M; Jander, R
2000-12-01
Previous studies have explored two-dimensional path integration in rodents by recording responses to passive rotation on a horizontal plane. This study adds the element of passive rotation in a vertical plane, necessitating the mouse to integrate positional information from three dimensions. Mice were trained to climb a wire mesh joining two horizontal planes. The whole arena was rotated 90 degrees while the mouse was vertically oriented as it moved between planes. Rotation was conducted both clockwise and counter-clockwise, controls being provided by rotation of the arena while the mouse was in its nest-box. All 16 mice tested altered their direction of travel subsequent to rotation in the vertical plane, compensating with a change in their path on the following horizontal plane.
Path integral Liouville dynamics for thermal equilibrium systems
Liu, Jian
2014-06-14
We show a new imaginary time path integral based method—path integral Liouville dynamics (PILD), which can be derived from the equilibrium Liouville dynamics [J. Liu and W. H. Miller, J. Chem. Phys. 134, 104101 (2011)] in the Wigner phase space. Numerical tests of PILD with the simple (white noise) Langevin thermostat have been made for two strongly anharmonic model problems. Since implementation of PILD does not request any specific form of the potential energy surface, the results suggest that PILD offers a potentially useful approach for general condensed phase molecular systems to have the two important properties: conserves the quantum canonical distribution and recovers exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits.
Path integral for the relativistic particle in curved space
NASA Astrophysics Data System (ADS)
Ferraro, Rafael
1992-02-01
The propagator for a single relativistic particle in a (D+1)-dimensional curved background is obtained by evaluating the canonical path integral in the true 2D-dimensional phase space. Since only paths moving forward in time are integrated, the resulting propagator depends on how the time is chosen; i.e., it depends on the reference system. In order for the propagator to satisfy the properties of a unitary theory, the time must be attached to a Killing vector. Although the measure is unique (it is the Liouville measure), the skeletonization of the phase-space functional action is ambiguous. One such ambiguity is exploited to obtain different propagators obeying the Klein-Gordon equation with different couplings to quantities related to the shape of the reference system (spatial curvature, etc.).
A path to integration in an academic health science center.
Panko, W B; Wilson, W
1992-01-01
This article describes a networking and integration strategy in use at the University of Michigan Medical Center. This strategy builds upon the existing technology base and is designed to provide a roadmap that will direct short-term development along a productive, long-term path. It offers a way to permit the short-term development of incremental solutions to current problems while at the same time maximizing the likelihood that these incremental efforts can be recycled into a more comprehensive approach.
Path integral analysis of Jarzynski's equality: analytical results.
Minh, David D L; Adib, Artur B
2009-02-01
We apply path integrals to study nonequilibrium work theorems in the context of Brownian dynamics, deriving in particular the equations of motion governing the most typical and most dominant trajectories. For the analytically soluble cases of a moving harmonic potential and a harmonic oscillator with a time-dependent natural frequency, we find such trajectories, evaluate the work-weighted propagators, and validate Jarzynski's equality.
Asymptotics of Selberg-like integrals by lattice path counting
Novaes, Marcel
2011-04-15
We obtain explicit expressions for positive integer moments of the probability density of eigenvalues of the Jacobi and Laguerre random matrix ensembles, in the asymptotic regime of large dimension. These densities are closely related to the Selberg and Selberg-like multidimensional integrals. Our method of solution is combinatorial: it consists in the enumeration of certain classes of lattice paths associated to the solution of recurrence relations.
Path integral approach to the quantum fidelity amplitude
2016-01-01
The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and in its applications, such as time-resolved electronic spectroscopy. We derive an exact path integral formula for the fidelity amplitude and use it to obtain a series of increasingly accurate semiclassical approximations by truncating an exact expansion of the path integral exponent. While the zeroth-order expansion results in a remarkably simple, yet non-trivial approximation for the fidelity amplitude, the first-order expansion yields an alternative derivation of the so-called ‘dephasing representation,’ circumventing the use of a semiclassical propagator as in the original derivation. We also obtain an approximate expression for fidelity based on the second-order expansion, which resolves several shortcomings of the dephasing representation. The rigorous derivation from the path integral permits the identification of sufficient conditions under which various approximations obtained become exact. PMID:27140973
Efficient stochastic thermostatting of path integral molecular dynamics.
Ceriotti, Michele; Parrinello, Michele; Markland, Thomas E; Manolopoulos, David E
2010-09-28
The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently developed colored noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nosé-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.
Path integral approach to the quantum fidelity amplitude.
Vaníček, Jiří; Cohen, Doron
2016-06-13
The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and in its applications, such as time-resolved electronic spectroscopy. We derive an exact path integral formula for the fidelity amplitude and use it to obtain a series of increasingly accurate semiclassical approximations by truncating an exact expansion of the path integral exponent. While the zeroth-order expansion results in a remarkably simple, yet non-trivial approximation for the fidelity amplitude, the first-order expansion yields an alternative derivation of the so-called 'dephasing representation,' circumventing the use of a semiclassical propagator as in the original derivation. We also obtain an approximate expression for fidelity based on the second-order expansion, which resolves several shortcomings of the dephasing representation. The rigorous derivation from the path integral permits the identification of sufficient conditions under which various approximations obtained become exact.
Efficient stochastic thermostatting of path integral molecular dynamics
NASA Astrophysics Data System (ADS)
Ceriotti, Michele; Parrinello, Michele; Markland, Thomas E.; Manolopoulos, David E.
2010-09-01
The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently developed colored noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nosé-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.
Electronic Stroke CarePath: Integrated Approach to Stroke Care.
Katzan, Irene L; Fan, Youran; Speck, Micheal; Morton, Johanna; Fromwiller, Lauren; Urchek, John; Uchino, Ken; Griffith, Sandra D; Modic, Michael
2015-10-01
We describe the development, implementation, and outcomes of the first 2 years of the Electronic Stroke CarePath, an initiative developed for management of ischemic stroke patients in an effort to improve efficiency and quality of care for patients. The CarePath consists of care pathways for ischemic stroke that are integrated within the electronic health record. Patient-reported outcomes are collected using an external software platform. Documentation tools, order sets, and clinical decision support were designed to improve efficiency, optimize process measure adherence, and produce clinical data as a byproduct of care that are available for future analyses. Inpatient mortality and length of stay were compared before and after CarePath implementation in ischemic stroke patients after adjustment for case-mix. Postdischarge functional outcomes of patients with ischemic stroke were compared between the first 3 months of rollout and remainder of the study period. From January 2011 to December 2012, there were 1106 patients with ischemic stroke on the CarePath. There was a decline in inpatient mortality in patients with ischemic stroke, but not in control patients with intracerebral or subarachnoid hemorrhage. Completion rate of patient-reported questionnaires at postdischarge stroke follow-up was 72.9%. There was a trend toward improved functional outcomes at follow-up with CarePath implementation. Implementation of the Electronic Stroke CarePath is feasible and may be associated with a benefit in multiple different outcomes after ischemic stroke. This approach may be an important strategy for optimizing stroke care in the future.
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Stringer, Simon M; Rolls, Edmund T
2006-12-01
A key issue is how networks in the brain learn to perform path integration, that is update a represented position using a velocity signal. Using head direction cells as an example, we show that a competitive network could self-organize to learn to respond to combinations of head direction and angular head rotation velocity. These combination cells can then be used to drive a continuous attractor network to the next head direction based on the incoming rotation signal. An associative synaptic modification rule with a short term memory trace enables preceding combination cell activity during training to be associated with the next position in the continuous attractor network. The network accounts for the presence of neurons found in the brain that respond to combinations of head direction and angular head rotation velocity. Analogous networks in the hippocampal system could self-organize to perform path integration of place and spatial view representations.
Path-integral approach to the Wigner-Kirkwood expansion.
Jizba, Petr; Zatloukal, Václav
2014-01-01
We study the high-temperature behavior of quantum-mechanical path integrals. Starting from the Feynman-Kac formula, we derive a functional representation of the Wigner-Kirkwood perturbation expansion for quantum Boltzmann densities. As shown by its applications to different potentials, the presented expansion turns out to be quite efficient in generating analytic form of the higher-order expansion coefficients. To put some flesh on the bare bones, we apply the expansion to obtain basic thermodynamic functions of the one-dimensional anharmonic oscillator. Further salient issues, such as generalization to the Bloch density matrix and comparison with the more customary world-line formulation, are discussed.
A path to integration in an academic health science center.
Panko, W. B.; Wilson, W.
1992-01-01
This article describes a networking and integration strategy in use at the University of Michigan Medical Center. This strategy builds upon the existing technology base and is designed to provide a roadmap that will direct short-term development along a productive, long-term path. It offers a way to permit the short-term development of incremental solutions to current problems while at the same time maximizing the likelihood that these incremental efforts can be recycled into a more comprehensive approach. PMID:1336413
Quantum corrections from a path integral over reparametrizations
Makeenko, Yuri; Olesen, Poul
2010-08-15
We study the path integral over reparametrizations that has been proposed as an ansatz for the Wilson loops in the large-N QCD and reproduces the area law in the classical limit of large loops. We show that a semiclassical expansion for a rectangular loop captures the Luescher term associated with d=26 dimensions and propose a modification of the ansatz that reproduces the Luescher term in other dimensions, which is observed in lattice QCD. We repeat the calculation for an outstretched ellipse advocating the emergence of an analog of the Luescher term and verify this result by a direct computation of the determinant of the Laplace operator and the conformal anomaly.
Path integral molecular dynamics at zero thermal temperature
NASA Astrophysics Data System (ADS)
Willow, Soohaeng Yoo
2017-04-01
Path integral molecular dynamics (PIMD) simulations at the zero thermal temperature still remain inconceivable. Herein, the quantum-mechanical partition function is revised in conjunction with the time-independent Schrödinger equation. The imaginary temperature for the quantum-mechanical partition function is introduced as an independent variable and defined under the guidance of the virial theorem. In the end, computational evidences are provided showing that this revised PIMD simulation at the zero thermal temperature reproduces both the zero-point energy and the probability density obtained from the Schrödinger equation for the harmonic oscillator.
Remarks on the Origin of Path Integration:. Einstein and Feynman
NASA Astrophysics Data System (ADS)
Sauer, T.
2008-11-01
I offer some historical comments about the origins of Feynman's path-integral approach, as an alternative approach to standard quantum mechanics. Looking at the interaction between Einstein and Feynman, which was mediated by Feynman's thesis supervisor John Wheeler, it is argued that, contrary to what one might expect, the significance of the interaction between Einstein and Feynman pertained to a critique of classical field theory, rather than to a direct critique of quantum mechanics itself. Nevertheless, the critical perspective on classical field theory became a motivation and point of departure for Feynman's space-time approach to non-relativistic quantum mechanics.
Path integral Monte Carlo on a lattice. II. Bound states
NASA Astrophysics Data System (ADS)
O'Callaghan, Mark; Miller, Bruce N.
2016-07-01
The equilibrium properties of a single quantum particle (qp) interacting with a classical gas for a wide range of temperatures that explore the system's behavior in the classical as well as in the quantum regime is investigated. Both the qp and the atoms are restricted to sites on a one-dimensional lattice. A path integral formalism developed within the context of the canonical ensemble is utilized, where the qp is represented by a closed, variable-step random walk on the lattice. Monte Carlo methods are employed to determine the system's properties. To test the usefulness of the path integral formalism, the Metropolis algorithm is employed to determine the equilibrium properties of the qp in the context of a square well potential, forcing the qp to occupy bound states. We consider a one-dimensional square well potential where all atoms on the lattice are occupied with one atom with an on-site potential except for a contiguous set of sites of various lengths centered at the middle of the lattice. Comparison of the potential energy, the energy fluctuations, and the correlation function are made between the results of the Monte Carlo simulations and the numerical calculations.
A note on the path integral representation for Majorana fermions
NASA Astrophysics Data System (ADS)
Greco, Andrés
2016-04-01
Majorana fermions are currently of huge interest in the context of nanoscience and condensed matter physics. Different to usual fermions, Majorana fermions have the property that the particle is its own anti-particle thus, they must be described by real fields. Mathematically, this property makes nontrivial the quantization of the problem due, for instance, to the absence of a Wick-like theorem. In view of the present interest on the subject, it is important to develop different theoretical approaches in order to study problems where Majorana fermions are involved. In this note we show that Majorana fermions can be studied in the context of field theories for constrained systems. Using the Faddeev-Jackiw formalism for quantum field theories with constraints, we derived the path integral representation for Majorana fermions. In order to show the validity of the path integral we apply it to an exactly solvable problem. This application also shows that it is rather simple to perform systematic calculations on the basis of the present framework.
Path-integral molecular dynamics simulation of diamond
NASA Astrophysics Data System (ADS)
Ramírez, Rafael; Herrero, Carlos P.; Hernández, Eduardo R.
2006-06-01
Diamond is studied by path-integral molecular dynamics simulations of the atomic nuclei in combination with a tight-binding Hamiltonian to describe its electronic structure and total energy. This approach allows us to quantify the influence of quantum zero-point vibrations and finite temperatures on both the electronic and vibrational properties of diamond. The electron-phonon coupling mediated by the zero-point vibration reduces the direct electronic gap of diamond by 10%. The calculated decrease of the direct gap with temperature shows good agreement with the experimental data available up to 700K . Anharmonic vibrational frequencies of the crystal have been obtained from a linear-response approach based on the path integral formalism. In particular, the temperature dependence of the zone-center optical phonon has been derived from the simulations. The anharmonicity of the interatomic potential produces a red shift of this phonon frequency. At temperatures above 500K , this shift is overestimated in comparison to available experimental data. The predicted temperature shift of the elastic constant c44 displays reasonable agreement with the available experimental results.
NASA Astrophysics Data System (ADS)
Wong, Kin-Yiu; Gao, Jiali
2007-12-01
Based on Kleinert's variational perturbation (KP) theory [Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 3rd ed. (World Scientific, Singapore, 2004)], we present an analytic path-integral approach for computing the effective centroid potential. The approach enables the KP theory to be applied to any realistic systems beyond the first-order perturbation (i.e., the original Feynman-Kleinert [Phys. Rev. A 34, 5080 (1986)] variational method). Accurate values are obtained for several systems in which exact quantum results are known. Furthermore, the computed kinetic isotope effects for a series of proton transfer reactions, in which the potential energy surfaces are evaluated by density-functional theory, are in good accordance with experiments. We hope that our method could be used by non-path-integral experts or experimentalists as a "black box" for any given system.
Potential theory, path integrals and the Laplacian of the indicator
NASA Astrophysics Data System (ADS)
Lange, Rutger-Jan
2012-11-01
This paper links the field of potential theory — i.e. the Dirichlet and Neumann problems for the heat and Laplace equation — to that of the Feynman path integral, by postulating the following seemingly ill-defined potential: V(x):=∓ {{σ^2}}/2nabla_x^2{1_{{xin D}}} where the volatility is the reciprocal of the mass (i.e. m = 1/ σ 2) and ħ = 1. The Laplacian of the indicator can be interpreted using the theory of distributions: it is the d-dimensional analogue of the Dirac δ'-function, which can formally be defined as partial_x^2{1_{x>0 }} . We show, first, that the path integral's perturbation series (or Born series) matches the classical single and double boundary layer series of potential theory, thereby connecting two hitherto unrelated fields. Second, we show that the perturbation series is valid for all domains D that allow Green's theorem (i.e. with a finite number of corners, edges and cusps), thereby expanding the classical applicability of boundary layers. Third, we show that the minus (plus) in the potential holds for the Dirichlet (Neumann) boundary condition; showing for the first time a particularly close connection between these two classical problems. Fourth, we demonstrate that the perturbation series of the path integral converges as follows:
Quantum Calisthenics: Gaussians, The Path Integral and Guided Numerical Approximations
Weinstein, Marvin; /SLAC
2009-02-12
It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way to understand how quantum mechanics works. I begin with an incredibly easy way to derive the time evolution of a Gaussian wave-packet for the case free and harmonic motion without any need to know the eigenstates of the Hamiltonian. This discussion is completely analytic and I will later use it to relate the solution for the behavior of the Gaussian packet to the Feynman path-integral and stationary phase approximation. It will be clear that using the information about the evolution of the Gaussian in this way goes far beyond what the stationary phase approximation tells us. Next, I introduce the concept of the bucket brigade approach to dealing with problems that cannot be handled totally analytically. This approach combines the intuition obtained in the initial discussion, as well as the intuition obtained from the path-integral, with simple numerical tools. My goal is to show that, for any specific process, there is a simple Hilbert space interpretation of the stationary phase approximation. I will then argue that, from the point of view of numerical approximations, the trajectory obtained from my generalization of the stationary phase approximation specifies that subspace of the full Hilbert space that is needed to compute the time evolution of the particular state under the full Hamiltonian. The prescription I will give is totally non-perturbative and we will see, by the grace of Maple animations computed for the case of the anharmonic oscillator Hamiltonian, that this approach allows surprisingly accurate computations to be performed with very little work. I think of this approach to the path-integral as defining what I call a guided numerical approximation scheme. After the discussion of the anharmonic oscillator I will
PhytoPath: an integrative resource for plant pathogen genomics
Pedro, Helder; Maheswari, Uma; Urban, Martin; Irvine, Alistair George; Cuzick, Alayne; McDowall, Mark D.; Staines, Daniel M.; Kulesha, Eugene; Hammond-Kosack, Kim Elizabeth; Kersey, Paul Julian
2016-01-01
PhytoPath (www.phytopathdb.org) is a resource for genomic and phenotypic data from plant pathogen species, that integrates phenotypic data for genes from PHI-base, an expertly curated catalog of genes with experimentally verified pathogenicity, with the Ensembl tools for data visualization and analysis. The resource is focused on fungi, protists (oomycetes) and bacterial plant pathogens that have genomes that have been sequenced and annotated. Genes with associated PHI-base data can be easily identified across all plant pathogen species using a BioMart-based query tool and visualized in their genomic context on the Ensembl genome browser. The PhytoPath resource contains data for 135 genomic sequences from 87 plant pathogen species, and 1364 genes curated for their role in pathogenicity and as targets for chemical intervention. Support for community annotation of gene models is provided using the WebApollo online gene editor, and we are working with interested communities to improve reference annotation for selected species. PMID:26476449
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2012-06-06
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Thermal Momentum Distribution from Path Integrals with Shifted Boundary Conditions
NASA Astrophysics Data System (ADS)
Giusti, Leonardo; Meyer, Harvey B.
2011-04-01
For a thermal field theory formulated in the grand canonical ensemble, the distribution of the total momentum is an observable characterizing the thermal state. We show that its cumulants are related to thermodynamic potentials. In a relativistic system, for instance, the thermal variance of the total momentum is a direct measure of the enthalpy. We relate the generating function of the cumulants to the ratio of (a) a partition function expressed as a Matsubara path integral with shifted boundary conditions in the compact direction and (b) the ordinary partition function. In this form the generating function is well suited for Monte Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang-Mills theory and obtain the entropy density at three different temperatures.
Coupled exciton-photon Bose condensate in path integral formalism
NASA Astrophysics Data System (ADS)
Elistratov, A. A.; Lozovik, Yu. E.
2016-03-01
We study the behavior of exciton polaritons in an optical microcavity with an embedded semiconductor quantum well. We use a two-component exciton-photon approach formulated in terms of path integral formalism. In order to describe spatial distributions of the exciton and photon condensate densities, the two coupled equations of the Gross-Pitaevskii type are derived. For a homogeneous system, we find the noncondensate photon and exciton spectra, calculate the coefficients of transformation from the exciton-photon basis to the lower-upper polariton basis, and obtain the exciton and photon occupation numbers of the lower and upper polariton branches for nonzero temperatures. For an inhomogeneous system, the set of coupled equations of the Bogoliubov-de Gennes type is derived. The equations govern the spectra and spatial distributions of noncondensate photons and excitons.
Path integral quantization corresponding to the deformed Heisenberg algebra
Pramanik, Souvik; Moussa, Mohamed; Faizal, Mir; Ali, Ahmed Farag
2015-11-15
In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.
Path integral approach to electron scattering in classical electromagnetic potential
NASA Astrophysics Data System (ADS)
Chuang, Xu; Feng, Feng; Ying-Jun, Li
2016-05-01
As is known to all, the electron scattering in classical electromagnetic potential is one of the most widespread applications of quantum theory. Nevertheless, many discussions about electron scattering are based upon single-particle Schrodinger equation or Dirac equation in quantum mechanics rather than the method of quantum field theory. In this paper, by using the path integral approach of quantum field theory, we perturbatively evaluate the scattering amplitude up to the second order for the electron scattering by the classical electromagnetic potential. The results we derive are convenient to apply to all sorts of potential forms. Furthermore, by means of the obtained results, we give explicit calculations for the one-dimensional electric potential. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374360, 11405266, and 11505285) and the National Basic Research Program of China (Grant No. 2013CBA01504).
Looping probabilities of elastic chains: a path integral approach.
Cotta-Ramusino, Ludovica; Maddocks, John H
2010-11-01
We consider an elastic chain at thermodynamic equilibrium with a heat bath, and derive an approximation to the probability density function, or pdf, governing the relative location and orientation of the two ends of the chain. Our motivation is to exploit continuum mechanics models for the computation of DNA looping probabilities, but here we focus on explaining the novel analytical aspects in the derivation of our approximation formula. Accordingly, and for simplicity, the current presentation is limited to the illustrative case of planar configurations. A path integral formalism is adopted, and, in the standard way, the first approximation to the looping pdf is obtained from a minimal energy configuration satisfying prescribed end conditions. Then we compute an additional factor in the pdf which encompasses the contributions of quadratic fluctuations about the minimum energy configuration along with a simultaneous evaluation of the partition function. The original aspects of our analysis are twofold. First, the quadratic Lagrangian describing the fluctuations has cross-terms that are linear in first derivatives. This, seemingly small, deviation from the structure of standard path integral examples complicates the necessary analysis significantly. Nevertheless, after a nonlinear change of variable of Riccati type, we show that the correction factor to the pdf can still be evaluated in terms of the solution to an initial value problem for the linear system of Jacobi ordinary differential equations associated with the second variation. The second novel aspect of our analysis is that we show that the Hamiltonian form of these linear Jacobi equations still provides the appropriate correction term in the inextensible, unshearable limit that is commonly adopted in polymer physics models of, e.g. DNA. Prior analyses of the inextensible case have had to introduce nonlinear and nonlocal integral constraints to express conditions on the relative displacement of the end
Age differences in virtual environment and real world path integration
Adamo, Diane E.; Briceño, Emily M.; Sindone, Joseph A.; Alexander, Neil B.; Moffat, Scott D.
2012-01-01
Accurate path integration (PI) requires the integration of visual, proprioceptive, and vestibular self-motion cues and age effects associated with alterations in processing information from these systems may contribute to declines in PI abilities. The present study investigated age-related differences in PI in conditions that varied as a function of available sources of sensory information. Twenty-two healthy, young (23.8 ± 3.0 years) and 16 older (70.1 ± 6.4 years) adults participated in distance reproduction and triangle completion tasks (TCTs) performed in a virtual environment (VE) and two “real world” conditions: guided walking and wheelchair propulsion. For walking and wheelchair propulsion conditions, participants wore a blindfold and wore noise-blocking headphones and were guided through the workspace by the experimenter. For the VE condition, participants viewed self-motion information on a computer monitor and used a joystick to navigate through the environment. For TCTs, older compared to younger individuals showed greater errors in rotation estimations performed in the wheelchair condition, and for rotation and distance estimations in the VE condition. Distance reproduction tasks (DRTs), in contrast, did not show any age effects. These findings demonstrate that age differences in PI vary as a function of the available sources of information and by the complexity of outbound pathway. PMID:23055969
The retrosplenial cortex is necessary for path integration in the dark.
Elduayen, Coralie; Save, Etienne
2014-10-01
An increasing amount of data indicates that the retrosplenial cortex (RSC) plays a role in navigation and spatial memory. Moreover, it has been suggested that the RSC integrates mnemonic spatial features of the environment with self-motion information therefore enabling accurate path integration in darkness. This hypothesis rests on data obtained from animals trained in spatial memory tasks involving the conjoint use of allothetic and idiothetic information [8]. We examined the contribution of the RSC when animals are submitted to a path integration task with minimal memory requirement in light and dark. We found that RSC-lesioned rats exhibited a path integration deficit in the dark but not in the light. This suggests that the RSC is important for path integration and incorporates visuospatial information to maintain path integration accuracy.
Keeping track of the distance from home by leaky integration along veering paths.
Lappe, Markus; Stiels, Maren; Frenz, Harald; Loomis, Jack M
2011-07-01
When humans use vision to gauge the travel distance of an extended forward movement, they often underestimate the movement's extent. This underestimation can be explained by leaky path integration, an integration of the movement to obtain distance. Distance underestimation occurs because this integration is imperfect and contains a leak that increases with distance traveled. We asked human observers to estimate the distance from a starting location for visually simulated movements in a virtual environment. The movements occurred along curved paths that veered left and right around a central forward direction. In this case, the distance that has to be integrated (i.e., the beeline distance between origin and endpoint) and the distance that is traversed (the path length along the curve) are distinct. We then tested whether the leak accumulated with distance from the origin or with traversed distance along the curved path. Leaky integration along the path makes the seemingly counterintuitive prediction that the estimated origin-to-endpoint distance should decrease with increasing veering, because the length of the path over which the integration occurs increases, leading to a larger leak effect. The results matched the prediction: movements of identical origin-to-endpoint distance were judged as shorter when the path became longer. We conclude that leaky path integration from visual motion is performed along the traversed path even when a straight beeline distance is calculated.
Quantum effects in graphene monolayers: Path-integral simulations.
Herrero, Carlos P; Ramírez, Rafael
2016-12-14
Path-integral molecular dynamics (PIMD) simulations have been carried out to study the influence of quantum dynamics of carbon atoms on the properties of a single graphene layer. Finite-temperature properties were analyzed in the range from 12 to 2000 K, by using the LCBOPII effective potential. To assess the magnitude of quantum effects in structural and thermodynamic properties of graphene, classical molecular dynamics simulations have been also performed. Particular emphasis has been laid on the atomic vibrations along the out-of-plane direction. Even though quantum effects are present in these vibrational modes, we show that at any finite temperature classical-like motion dominates over quantum delocalization, provided that the system size is large enough. Vibrational modes display an appreciable anharmonicity, as derived from a comparison between kinetic and potential energies of the carbon atoms. Nuclear quantum effects are found to be appreciable in the interatomic distance and layer area at finite temperatures. The thermal expansion coefficient resulting from PIMD simulations vanishes in the zero-temperature limit, in agreement with the third law of thermodynamics.
Path integrals, matter waves, and the double slit
NASA Astrophysics Data System (ADS)
Jones, Eric R.; Bach, Roger A.; Batelaan, Herman
2015-11-01
Basic explanations of the double slit diffraction phenomenon include a description of waves that emanate from two slits and interfere. The locations of the interference minima and maxima are determined by the phase difference of the waves. An optical wave, which has a wavelength λ and propagates a distance L, accumulates a phase of 2π L/λ . A matter wave, also having wavelength λ that propagates the same distance L, accumulates a phase of π L/λ , which is a factor of two different from the optical case. Nevertheless, in most situations, the phase difference, {{Δ }}\\varphi , for interfering matter waves that propagate distances that differ by {{Δ }}L, is approximately 2π {{Δ }}L/λ , which is the same value computed in the optical case. The difference between the matter and optical case hinders conceptual explanations of diffraction from two slits based on the matter-optics analogy. In the following article we provide a path integral description for matter waves with a focus on conceptual explanation. A thought experiment is provided to illustrate the validity range of the approximation {{Δ }}\\varphi ≈ 2π {{Δ }}L/λ .
Isotope effects in ice Ih: a path-integral simulation.
Herrero, Carlos P; Ramírez, Rafael
2011-03-07
Ice Ih has been studied by path-integral molecular dynamics simulations, using the effective q-TIP4P/F potential model for flexible water. This has allowed us to analyze finite-temperature quantum effects in this solid phase from 25 to 300 K at ambient pressure. Among these effects we find a negative thermal expansion of ice at low temperatures, which does not appear in classical molecular dynamics simulations. The compressibility derived from volume fluctuations gives results in line with experimental data. We have analyzed isotope effects in ice Ih by considering normal, heavy, and tritiated water. In particular, we studied the effect of changing the isotopic mass of hydrogen on the kinetic energy and atomic delocalization in the crystal as well as on structural properties such as interatomic distances and molar volume. For D(2)O ice Ih at 100 K we obtained a decrease in molar volume and intramolecular O-H distance of 0.6% and 0.4%, respectively, as compared to H(2)O ice.
Path integral regularization of pure Yang-Mills theory
Jacquot, J. L.
2009-07-15
In enlarging the field content of pure Yang-Mills theory to a cutoff dependent matrix valued complex scalar field, we construct a vectorial operator, which is by definition invariant with respect to the gauge transformation of the Yang-Mills field and with respect to a Stueckelberg type gauge transformation of the scalar field. This invariant operator converges to the original Yang-Mills field as the cutoff goes to infinity. With the help of cutoff functions, we construct with this invariant a regularized action for the pure Yang-Mills theory. In order to be able to define both the gauge and scalar fields kinetic terms, other invariant terms are added to the action. Since the scalar fields flat measure is invariant under the Stueckelberg type gauge transformation, we obtain a regularized gauge-invariant path integral for pure Yang-Mills theory that is mathematically well defined. Moreover, the regularized Ward-Takahashi identities describing the dynamics of the gauge fields are exactly the same as the formal Ward-Takahashi identities of the unregularized theory.
Computational Convergence of the Path Integral for Real Dendritic Morphologies
2012-01-01
Neurons are characterised by a morphological structure unique amongst biological cells, the core of which is the dendritic tree. The vast number of dendritic geometries, combined with heterogeneous properties of the cell membrane, continue to challenge scientists in predicting neuronal input-output relationships, even in the case of sub-threshold dendritic currents. The Green’s function obtained for a given dendritic geometry provides this functional relationship for passive or quasi-active dendrites and can be constructed by a sum-over-trips approach based on a path integral formalism. In this paper, we introduce a number of efficient algorithms for realisation of the sum-over-trips framework and investigate the convergence of these algorithms on different dendritic geometries. We demonstrate that the convergence of the trip sampling methods strongly depends on dendritic morphology as well as the biophysical properties of the cell membrane. For real morphologies, the number of trips to guarantee a small convergence error might become very large and strongly affect computational efficiency. As an alternative, we introduce a highly-efficient matrix method which can be applied to arbitrary branching structures. PMID:23174188
Quantum effects in graphene monolayers: Path-integral simulations
NASA Astrophysics Data System (ADS)
Herrero, Carlos P.; Ramírez, Rafael
2016-12-01
Path-integral molecular dynamics (PIMD) simulations have been carried out to study the influence of quantum dynamics of carbon atoms on the properties of a single graphene layer. Finite-temperature properties were analyzed in the range from 12 to 2000 K, by using the LCBOPII effective potential. To assess the magnitude of quantum effects in structural and thermodynamic properties of graphene, classical molecular dynamics simulations have been also performed. Particular emphasis has been laid on the atomic vibrations along the out-of-plane direction. Even though quantum effects are present in these vibrational modes, we show that at any finite temperature classical-like motion dominates over quantum delocalization, provided that the system size is large enough. Vibrational modes display an appreciable anharmonicity, as derived from a comparison between kinetic and potential energies of the carbon atoms. Nuclear quantum effects are found to be appreciable in the interatomic distance and layer area at finite temperatures. The thermal expansion coefficient resulting from PIMD simulations vanishes in the zero-temperature limit, in agreement with the third law of thermodynamics.
Barbero-Immirzi parameter, manifold invariants and Euclidean path integrals
NASA Astrophysics Data System (ADS)
Liko, Tomáš
2012-05-01
The Barbero-Immirzi parameter γ appears in the real connection formulation of gravity in terms of the Ashtekar variables, and gives rise to a one-parameter quantization ambiguity in loop quantum gravity. In this paper, we investigate the conditions under which γ will have physical effects in Euclidean quantum gravity. This is done by constructing a well-defined Euclidean path integral for the Holst action with a non-zero cosmological constant on a manifold with a boundary. We find that two general conditions must be satisfied by the spacetime manifold in order for the Holst action and its surface integral to be non-zero: (i) the metric has to be non-diagonalizable; (ii) the Pontryagin number of the manifold has to be non-zero. The latter is a strong topological condition and rules out many of the known solutions to the Einstein field equations. This result leads us to evaluate the on-shell first-order Holst action and corresponding Euclidean partition function on the Taub-NUT-ADS solution. We find that γ shows up as a finite rotation of the on-shell partition function which corresponds to shifts in the energy and entropy of the NUT charge. In an appendix, we also evaluate the Holst action on the Taub-NUT and Taub-bolt solutions in flat spacetime and find that in that case as well γ shows up in the energy and entropy of the NUT and bolt charges. We also present an example whereby the Euler characteristic of the manifold has a non-trivial effect on black hole mergers. Communicated by PRLV Moniz
Path-integral approach to 't Hooft's derivation of quantum physics from classical physics
Blasone, Massimo; Jizba, Petr; Kleinert, Hagen
2005-05-15
We present a path-integral formulation of 't Hooft's derivation of quantum physics from classical physics. The crucial ingredient of this formulation is Gozzi et al.'s supersymmetric path integral of classical mechanics. We quantize explicitly two simple classical systems: the planar mathematical pendulum and the Roessler dynamical system.
Factors Affecting Counselor Educators' Integration of Educational Technology: A Path Analysis
ERIC Educational Resources Information Center
Kennedy, John F.
2011-01-01
This study used path analysis to explore the effects of individual and institutional-level factors on counselor educators' integration of technology in counselor education. The study fills a gap in the literature by providing a research-based path model describing counselor educators' integration of technology in counselor education. Counselor…
Color path-integral Monte Carlo simulations of quark-gluon plasma
NASA Astrophysics Data System (ADS)
Filinov, V. S.; Ivanov, Yu. B.; Bonitz, M.; Fortov, V. E.; Levashov, P. R.
2012-02-01
Thermodynamic properties of a strongly coupled quark-gluon plasma (QGP) of constituent quasiparticles are studied by a color path-integral Monte Carlo simulations (CPIMC). For our simulations we have presented QGP partition function in the form of color path integral with new relativistic measure instead of Gaussian one used in Feynman and Wiener path integrals. For integration over color variable we have also developed procedure of sampling color variables according to the group SU(3) Haar measure. It is shown that this method is able to reproduce the available quantum lattice chromodynamics (QCD) data.
NASA Astrophysics Data System (ADS)
Haftbaradaran, Hamed; Qu, Jianmin
2014-11-01
In this study, we first demonstrate that the J-integral in classical linear elasticity becomes path-dependent when the solid is subjected to combined electrical, chemical and mechanical loadings. We then construct an electro-chemo-mechanical J-integral that is path-independent under such combined multiple driving forces. Further, we show that this electro-chemo-mechanical J-integral represents the rate at which the grand potential releases per unit crack growth. As an example, the path-independent nature of the electro-chemo-mechanical J-integral is demonstrated by solving the problem of a thin elastic film delaminated from a thick elastic substrate.
Square-root actions, metric signature, and the path integral of quantum gravity
NASA Astrophysics Data System (ADS)
Carlini, A.; Greensite, J.
1995-12-01
We consider quantization of the Baierlein-Sharp-Wheeler form of the gravitational action, in which the lapse function is determined from the Hamiltonian constraint. This action has a square root form, analogous to the actions of the relativistic particle and Nambu string. We argue that path-integral quantization of the gravitational action should be based on a path integrand exp[ √i S] rather than the familiar Feynman expression exp[iS], and that unitarity requires integration over manifolds of both Euclidean and Lorentzian signature. We discuss the relation of this path integral to our previous considerations regarding the problem of time, and extend our approach to include fermions.
Piloting and Path Integration within and across Boundaries
ERIC Educational Resources Information Center
Mou, Weimin; Wang, Lin
2015-01-01
Three experiments investigated whether navigation is less efficient across boundaries than within boundaries. In an immersive virtual environment, participants learned objects' locations in a large room or a small room. Participants then pointed to the objects' original locations after physically walking a circuitous path without vision.…
A brief view of known landmarks reorientates path integration in hamsters
NASA Astrophysics Data System (ADS)
Etienne, A. S.; Boulens, V.; Maurer, R.; Rowe, T.; Siegrist, C.
In darkness, hamsters commute between their nest and a feeding site through path integration only, and therefore show cumulative errors in the return direction to the nest. We examined whether a brief presentation of familiar room cues could reset the path integrator. The hamsters could see the room cues either during, or at the end of, the outward journey to the food place, in a conflict situation where motion cues and visual information were set at variance. In both conditions, the animals used mainly visual information to return home. Thus, hamsters can determine their azimuth, and possibly their location, through a visual fix, and can reset their path integrator through the fix. This allows them to update their position during further locomotion in the dark and thus to compute a correct homing vector with respect to a visually induced reference frame. Taking episodic positional fixes may greatly enhance the functional value of path integration.
A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat.
Liu, Jian; Li, Dezhang; Liu, Xinzijian
2016-07-14
We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used.
A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat
NASA Astrophysics Data System (ADS)
Liu, Jian; Li, Dezhang; Liu, Xinzijian
2016-07-01
We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used.
Rotational error in path integration: encoding and execution errors in angle reproduction.
Chrastil, Elizabeth R; Warren, William H
2017-03-16
Path integration is fundamental to human navigation. When a navigator leaves home on a complex outbound path, they are able to keep track of their approximate position and orientation and return to their starting location on a direct homebound path. However, there are several sources of error during path integration. Previous research has focused almost exclusively on encoding error-the error in registering the outbound path in memory. Here, we also consider execution error-the error in the response, such as turning and walking a homebound trajectory. In two experiments conducted in ambulatory virtual environments, we examined the contribution of execution error to the rotational component of path integration using angle reproduction tasks. In the reproduction tasks, participants rotated once and then rotated again to face the original direction, either reproducing the initial turn or turning through the supplementary angle. One outstanding difficulty in disentangling encoding and execution error during a typical angle reproduction task is that as the encoding angle increases, so does the required response angle. In Experiment 1, we dissociated these two variables by asking participants to report each encoding angle using two different responses: by turning to walk on a path parallel to the initial facing direction in the same (reproduction) or opposite (supplementary angle) direction. In Experiment 2, participants reported the encoding angle by turning both rightward and leftward onto a path parallel to the initial facing direction, over a larger range of angles. The results suggest that execution error, not encoding error, is the predominant source of error in angular path integration. These findings also imply that the path integrator uses an intrinsic (action-scaled) rather than an extrinsic (objective) metric.
Which way and how far? Tracking of translation and rotation information for human path integration.
Chrastil, Elizabeth R; Sherrill, Katherine R; Hasselmo, Michael E; Stern, Chantal E
2016-10-01
Path integration, the constant updating of the navigator's knowledge of position and orientation during movement, requires both visuospatial knowledge and memory. This study aimed to develop a systems-level understanding of human path integration by examining the basic building blocks of path integration in humans. To achieve this goal, we used functional imaging to examine the neural mechanisms that support the tracking and memory of translational and rotational components of human path integration. Critically, and in contrast to previous studies, we examined movement in translation and rotation tasks with no defined end-point or goal. Navigators accumulated translational and rotational information during virtual self-motion. Activity in hippocampus, retrosplenial cortex (RSC), and parahippocampal cortex (PHC) increased during both translation and rotation encoding, suggesting that these regions track self-motion information during path integration. These results address current questions regarding distance coding in the human brain. By implementing a modified delayed match to sample paradigm, we also examined the encoding and maintenance of path integration signals in working memory. Hippocampus, PHC, and RSC were recruited during successful encoding and maintenance of path integration information, with RSC selective for tasks that required processing heading rotation changes. These data indicate distinct working memory mechanisms for translation and rotation, which are essential for updating neural representations of current location. The results provide evidence that hippocampus, PHC, and RSC flexibly track task-relevant translation and rotation signals for path integration and could form the hub of a more distributed network supporting spatial navigation. Hum Brain Mapp 37:3636-3655, 2016. © 2016 Wiley Periodicals, Inc.
A variational path integral molecular dynamics study of a solid helium-4
NASA Astrophysics Data System (ADS)
Miura, Shinichi
2011-01-01
In the present study, a variational path integral molecular dynamics method developed by the author [Chem. Phys. Lett. 482 (2009) 165] is applied to a solid helium-4 in the ground state. The method is a molecular dynamics algorithm for a variational path integral method which can be used to generate the exact ground state numerically. The solid state is shown to successfully be realized by the method, although a poor trial wavefunction that cannot describe the solid state is used.
Pérez, Alejandro; von Lilienfeld, O Anatole
2011-08-09
Thermodynamic integration, perturbation theory, and λ-dynamics methods were applied to path integral molecular dynamics calculations to investigate free energy differences due to "alchemical" transformations. Several estimators were formulated to compute free energy differences in solvable model systems undergoing changes in mass and/or potential. Linear and nonlinear alchemical interpolations were used for the thermodynamic integration. We find improved convergence for the virial estimators, as well as for the thermodynamic integration over nonlinear interpolation paths. Numerical results for the perturbative treatment of changes in mass and electric field strength in model systems are presented. We used thermodynamic integration in ab initio path integral molecular dynamics to compute the quantum free energy difference of the isotope transformation in the Zundel cation. The performance of different free energy methods is discussed.
Phase-space path-integral calculation of the Wigner function
NASA Astrophysics Data System (ADS)
Samson, J. H.
2003-10-01
The Wigner function W(q, p) is formulated as a phase-space path integral, whereby its sign oscillations can be seen to follow from interference between the geometrical phases of the paths. The approach has similarities to the path-centroid method in the configuration-space path integral. Paths can be classified by the midpoint of their ends; short paths where the midpoint is close to (q, p) and which lie in regions of low energy (low P function of the Hamiltonian) will dominate, and the enclosed area will determine the sign of the Wigner function. As a demonstration, the method is applied to a sequence of density matrices interpolating between a Poissonian number distribution and a number state, each member of which can be represented exactly by a discretized path integral with a finite number of vertices. Saddle-point evaluation of these integrals recovers (up to a constant factor) the WKB approximation to the Wigner function of a number state.
Trouvé, Hélène; Couturier, Yves; Etheridge, Francis; Saint-Jean, Olivier; Somme, Dominique
2010-01-01
Background The literature on integration indicates the need for an enhanced theorization of institutional integration. This article proposes path dependence as an analytical framework to study the systems in which integration takes place. Purpose PRISMA proposes a model for integrating health and social care services for older adults. This model was initially tested in Quebec. The PRISMA France study gave us an opportunity to analyze institutional integration in France. Methods A qualitative approach was used. Analyses were based on semi-structured interviews with actors of all levels of decision-making, observations of advisory board meetings, and administrative documents. Results Our analyses revealed the complexity and fragmentation of institutional integration. The path dependency theory, which analyzes the change capacity of institutions by taking into account their historic structures, allows analysis of this situation. The path dependency to the Bismarckian system and the incomplete reforms of gerontological policies generate the coexistence and juxtaposition of institutional systems. In such a context, no institution has sufficient ability to determine gerontology policy and build institutional integration by itself. Conclusion Using path dependence as an analytical framework helps to understand the reasons why institutional integration is critical to organizational and clinical integration, and the complex construction of institutional integration in France. PMID:20689740
Wang, Qian; Hammes-Schiffer, Sharon
2006-11-14
A hybrid quantum/classical path integral Monte Carlo (QC-PIMC) method for calculating the quantum free energy barrier for hydrogen transfer reactions in condensed phases is presented. In this approach, the classical potential of mean force along a collective reaction coordinate is calculated using umbrella sampling techniques in conjunction with molecular dynamics trajectories propagated according to a mapping potential. The quantum contribution is determined for each configuration along the classical trajectory with path integral Monte Carlo calculations in which the beads move according to an effective mapping potential. This type of path integral calculation does not utilize the centroid constraint and can lead to more efficient sampling of the relevant region of conformational space than free-particle path integral sampling. The QC-PIMC method is computationally practical for large systems because the path integral sampling for the quantum nuclei is performed separately from the classical molecular dynamics sampling of the entire system. The utility of the QC-PIMC method is illustrated by an application to hydride transfer in the enzyme dihydrofolate reductase. A comparison of this method to the quantized classical path and grid-based methods for this system is presented.
The development of path integration: combining estimations of distance and heading.
Smith, Alastair D; McKeith, Laura; Howard, Christina J
2013-12-01
Efficient daily navigation is underpinned by path integration, the mechanism by which we use self-movement information to update our position in space. This process is well understood in adulthood, but there has been relatively little study of path integration in childhood, leading to an underrepresentation in accounts of navigational development. Previous research has shown that calculation of distance and heading both tend to be less accurate in children as they are in adults, although there have been no studies of the combined calculation of distance and heading that typifies naturalistic path integration. In the present study, 5-year-olds and 7-year-olds took part in a triangle-completion task, where they were required to return to the start point of a multi-element path using only idiothetic information. Performance was compared to a sample of adult participants, who were found to be more accurate than children on measures of landing error, heading error, and distance error. Seven-year-olds were significantly more accurate than 5-year-olds on measures of landing error and heading error, although the difference between groups was much smaller for distance error. All measures were reliably correlated with age, demonstrating a clear development of path integration abilities within the age range tested. Taken together, these data make a strong case for the inclusion of path integration within developmental models of spatial navigational processing.
Quantum-classical path integral. I. Classical memory and weak quantum nonlocality.
Lambert, Roberto; Makri, Nancy
2012-12-14
We consider rigorous path integral descriptions of the dynamics of a quantum system coupled to a polyatomic environment, assuming that the latter is well approximated by classical trajectories. Earlier work has derived semiclassical or purely classical expressions for the influence functional from the environment, which should be sufficiently accurate for many situations, but the evaluation of quantum-(semi)classical path integral (QCPI) expressions has not been practical for large-scale simulation because the interaction with the environment introduces couplings nonlocal in time. In this work, we analyze the nature of the effects on a system from its environment in light of the observation [N. Makri, J. Chem. Phys. 109, 2994 (1998)] that true nonlocality in the path integral is a strictly quantum mechanical phenomenon. If the environment is classical, the path integral becomes local and can be evaluated in a stepwise fashion along classical trajectories of the free solvent. This simple "classical path" limit of QCPI captures fully the decoherence of the system via a classical mechanism. Small corrections to the classical path QCPI approximation may be obtained via an inexpensive random hop QCPI model, which accounts for some "back reaction" effects. Exploiting the finite length of nonlocality, we argue that further inclusion of quantum decoherence is possible via an iterative evaluation of the path integral. Finally, we show that the sum of the quantum amplitude factors with respect to the system paths leads to a smooth integrand as a function of trajectory initial conditions, allowing the use of Monte Carlo methods for the multidimensional phase space integral.
Bennett, Ilana J; Stark, Craig E L
2016-03-01
Pattern separation describes the orthogonalization of similar inputs into unique, non-overlapping representations. This computational process is thought to serve memory by reducing interference and to be mediated by the dentate gyrus of the hippocampus. Using ultra-high in-plane resolution diffusion tensor imaging (hrDTI) in older adults, we previously demonstrated that integrity of the perforant path, which provides input to the dentate gyrus from entorhinal cortex, was associated with mnemonic discrimination, a behavioral outcome designed to load on pattern separation. The current hrDTI study assessed the specificity of this perforant path integrity-mnemonic discrimination relationship relative to other cognitive constructs (identified using a factor analysis) and white matter tracts (hippocampal cingulum, fornix, corpus callosum) in 112 healthy adults (20-87 years). Results revealed age-related declines in integrity of the perforant path and other medial temporal lobe (MTL) tracts (hippocampal cingulum, fornix). Controlling for global effects of brain aging, perforant path integrity related only to the factor that captured mnemonic discrimination performance. Comparable integrity-mnemonic discrimination relationships were also observed for the hippocampal cingulum and fornix. Thus, whereas perforant path integrity specifically relates to mnemonic discrimination, mnemonic discrimination may be mediated by a broader MTL network.
Bennett, Ilana J.; Stark, Craig E.L.
2015-01-01
Pattern separation describes the orthogonalization of similar inputs into unique, non-overlapping representations. This computational process is thought to serve memory by reducing interference and to be mediated by the dentate gyrus of the hippocampus. Using ultra-high in-plane resolution diffusion tensor imaging (hrDTI) in older adults, we previously demonstrated that integrity of the perforant path, which provides input to the dentate gyrus from entorhinal cortex, was associated with mnemonic discrimination, a behavioral outcome designed to load on pattern separation. The current hrDTI study assessed the specificity of this perforant path integrity-mnemonic discrimination relationship relative to other cognitive constructs (identified using a factor analysis) and white matter tracts (hippocampal cingulum, fornix, corpus callosum) in 112 healthy adults (20–87 years). Results revealed age-related declines in integrity of the perforant path and other medial temporal lobe (MTL) tracts (hippocampal cingulum, fornix). Controlling for global effects of brain aging, perforant path integrity related only to the factor that captured mnemonic discrimination performance. Comparable integrity-mnemonic discrimination relationships were also observed for the hippocampal cingulum and fornix. Thus, whereas perforant path integrity specifically relates to mnemonic discrimination, mnemonic discrimination may be mediated by a broader MTL network. PMID:26149893
Quantum-classical path integral with self-consistent solvent-driven reference propagators.
Banerjee, Tuseeta; Makri, Nancy
2013-10-24
Efficient procedures for evaluating the quantum-classical path integral (QCPI) [J. Chem. Phys. 2013, 137, 22A552] are described. The main idea is to identify a trajectory-specific reference Hamiltonian that captures the dominant effects of the classical "solvent" degrees of freedom on the dynamics of the quantum "system". This time-dependent reference is used to construct a system propagator that is valid for large time increments. Residual "quantum memory" interactions are included via the path integral representation of the density matrix, which converges with large time steps. Two physically motivated reference schemes are considered. The first involves the dynamics of the solvent unperturbed by the system, which forms the basis for the "classical path" approximation. The second is based on solvent trajectories determined self-consistently with the evolution of the system, according to the time-dependent self-consistent field or Ehrenfest model. Application to dissipative two-level systems indicates that both reference schemes allow a substantial increase of the path integral time step, leading to rapid convergence of the path sum. In addition, the time-dependent reference propagators automatically weigh state-to-state coupling against solvent reorganization in the determination of transition probabilities, further enhancing the convergence of the path integral.
Application of path-independent integrals to elevated temperature crack growth
NASA Technical Reports Server (NTRS)
Kim, K. S.; Van Stone, R. H.
1990-01-01
The applicability of the J-integral in elasto-plastic fracture mechanics is limited to isothermal, monotonic loading conditions from the theoretical viewpoint, while in many applications, for instance gas turbine engines, crack growth occurs in the presence of cyclic inelastic loading, thermomechanical loading and temperature gradients. A number of path-independent (P-I) integrals have been proposed which do not have the restrictions of the J-integral. A review indicates that four of these integrals, although they are not the classical conservation integrals, are path-independent under these complex loading conditions. This paper describes a combined analytical and experimental effort to evaluate the ability of these four P-I integrals to correlate the crack growth data of Alloy 718 at elevated temperatures. Results for uniform temperature, 538 C, cases indicate that all these integrals are capable of correlating the crack growth data over a wide range of cyclic plasticity.
Automatic Tool Path Generation for Robot Integrated Surface Sculpturing System
NASA Astrophysics Data System (ADS)
Zhu, Jiang; Suzuki, Ryo; Tanaka, Tomohisa; Saito, Yoshio
In this paper, a surface sculpturing system based on 8-axis robot is proposed, the CAD/CAM software and tool path generation algorithm for this sculpturing system are presented. The 8-axis robot is composed of a 6-axis manipulator and a 2-axis worktable, it carves block of polystyrene foams by heated cutting tools. Multi-DOF (Degree of Freedom) robot benefits from the faster fashion than traditional RP (Rapid Prototyping) methods and more flexibility than CNC machining. With its flexibility driven from an 8-axis configuration, as well as efficient custom-developed software for rough cutting and finish cutting, this surface sculpturing system can carve sculptured surface accurately and efficiently.
Data Integration: Charting a Path Forward to 2035
2011-02-14
15 Figure 5: Data Architecture and Semantic Integration Framework……………………………...16 Figure 6: Depiction of...leadership and ability to execute. 6 Gartner defines the discipline of data integration as ―practices, architectural techniques and tools for...knowledge creation becomes possible. Finally, data models are the backbone of data architecture and are necessary, but also a key challenge to
SU(2) Coherent State Path Integrals Labeled by a Full Set of Euler Angles: Basic Formulation
NASA Astrophysics Data System (ADS)
Matsumoto, Masao
2012-11-01
We develop a basic formulation of the spin (SU(2)) coherent state path integrals based not on the conventional highest or lowest weight vectors but on arbitrary fiducial vectors. The coherent states, being defined on a 3-sphere, are specified by a full set of Euler angles. They are generally considered as states without classical analogues. The overcompleteness relation holds for the states, by which we obtain the time evolution of general systems in terms of the path integral representation; the resultant Lagrangian in the action has a monopole-type term à la Balachandran et al. as well as some additional terms, both of which depend on fiducial vectors in a simple way. The process of the discrete path integrals to the continuous ones is clarified. Complex variable forms of the states and path integrals are also obtained. During the course of all steps, we emphasize the analogies and correspondences to the general canonical coherent states and path integrals that we proposed some time ago. In this paper we concentrate on the basic formulation. The physical applications as well as criteria in choosing fiducial vectors for real Lagrangians, in relation to fictitious monopoles and geometric phases, will be treated in subsequent papers separately.
A path-integral Langevin equation treatment of low-temperature doped helium clusters
NASA Astrophysics Data System (ADS)
Ing, Christopher; Hinsen, Konrad; Yang, Jing; Zeng, Toby; Li, Hui; Roy, Pierre-Nicholas
2012-06-01
We present an implementation of path integral molecular dynamics for sampling low temperature properties of doped helium clusters using Langevin dynamics. The robustness of the path integral Langevin equation and white-noise Langevin equation [M. Ceriotti, M. Parrinello, T. E. Markland, and D. E. Manolopoulos, J. Chem. Phys. 133, 124104 (2010)], 10.1063/1.3489925 sampling methods are considered for those weakly bound systems with comparison to path integral Monte Carlo (PIMC) in terms of efficiency and accuracy. Using these techniques, convergence studies are performed to confirm the systematic error reduction introduced by increasing the number of discretization steps of the path integral. We comment on the structural and energetic evolution of HeN-CO2 clusters from N = 1 to 20. To quantify the importance of both rotations and exchange in our simulations, we present a chemical potential and calculated band origin shifts as a function of cluster size utilizing PIMC sampling that includes these effects. This work also serves to showcase the implementation of path integral simulation techniques within the molecular modelling toolkit [K. Hinsen, J. Comp. Chem. 21, 79 (2000)], 10.1002/(SICI)1096-987X(20000130)21:2<79::AID-JCC1>3.0.CO;2-B, an open-source molecular simulation package.
NASA Astrophysics Data System (ADS)
Utama, Briandhika; Purqon, Acep
2016-08-01
Path Integral is a method to transform a function from its initial condition to final condition through multiplying its initial condition with the transition probability function, known as propagator. At the early development, several studies focused to apply this method for solving problems only in Quantum Mechanics. Nevertheless, Path Integral could also apply to other subjects with some modifications in the propagator function. In this study, we investigate the application of Path Integral method in financial derivatives, stock options. Black-Scholes Model (Nobel 1997) was a beginning anchor in Option Pricing study. Though this model did not successfully predict option price perfectly, especially because its sensitivity for the major changing on market, Black-Scholes Model still is a legitimate equation in pricing an option. The derivation of Black-Scholes has a high difficulty level because it is a stochastic partial differential equation. Black-Scholes equation has a similar principle with Path Integral, where in Black-Scholes the share's initial price is transformed to its final price. The Black-Scholes propagator function then derived by introducing a modified Lagrange based on Black-Scholes equation. Furthermore, we study the correlation between path integral analytical solution and Monte-Carlo numeric solution to find the similarity between this two methods.
NASA Astrophysics Data System (ADS)
Halliwell, J. J.; Yearsley, J. M.
2013-06-01
Path integrals appear to offer natural and intuitively appealing methods for defining quantum-mechanical amplitudes for questions involving spacetime regions. For example, the amplitude for entering a spatial region during a given time interval is typically defined by summing over all paths between given initial and final points but restricting them to pass through the region at any time. We argue that there is, however, under very general conditions, a significant complication in such constructions. This is the fact that the concrete implementation of the restrictions on paths over an interval of time corresponds, in an operator language, to sharp monitoring at every moment of time in the given time interval. Such processes suffer from the quantum Zeno effect - the continual monitoring of a quantum system in a Hilbert subspace prevents its state from leaving that subspace. As a consequence, path integral amplitudes defined in this seemingly obvious way have physically and intuitively unreasonable properties and in particular, no sensible classical limit. In this paper we describe this frequently-occurring but little-appreciated phenomenon in some detail, showing clearly the connection with the quantum Zeno effect. We then show that it may be avoided by implementing the restriction on paths in the path integral in a "softer" way. The resulting amplitudes then involve a new coarse graining parameter, which may be taken to be a timescale epsilon, describing the softening of the restrictions on the paths. We argue that the complications arising from the Zeno effect are then negligible as long as epsilon >> 1/E, where E is the energy scale of the incoming state. Our criticisms of path integral constructions largely apply to approaches to quantum theory such as the decoherent histories approach or quantum measure theory, which do not specifically involve measurements. We address some criticisms of our approach by Sokolovksi, concerning the relevance of our results to
Path integral in area tensor Regge calculus and complex connections
NASA Astrophysics Data System (ADS)
Khatsymovsky, V. M.
2006-06-01
Euclidean quantum measure in Regge calculus with independent area tensors is considered using example of the Regge manifold of a simple structure. We go over to integrations along certain contours in the hyperplane of complex connection variables. Discrete connection and curvature on classical solutions of the equations of motion are not, strictly speaking, genuine connection and curvature, but more general quantities and, therefore, these do not appear as arguments of a function to be averaged, but are the integration (dummy) variables. We argue that upon integrating out the latter the resulting measure can be well-defined on physical hypersurface (for the area tensors corresponding to certain edge vectors, i.e. to certain metric) as positive and having exponential cutoff at large areas on condition that we confine ourselves to configurations which do not pass through degenerate metrics.
Travel distance estimation from visual motion by leaky path integration.
Lappe, Markus; Jenkin, Michael; Harris, Laurence R
2007-06-01
Visual motion can be a cue to travel distance when the motion signals are integrated. Distance estimates from visually simulated self-motion are imprecise, however. Previous work in our labs has given conflicting results on the imprecision: experiments by Frenz and Lappe had suggested a general underestimation of travel distance, while results from Redlick, Jenkin and Harris had shown an overestimation of travel distance. Here we describe a collaborative study that resolves the conflict by tracing it to differences in the tasks given to the subjects. With an identical set of subjects and identical visual motion simulation we show that underestimation of travel distance occurs when the task involves a judgment of distance from the starting position, and that overestimation of travel distance occurs when the task requires a judgment of the remaining distance to a particular target position. We present a leaky integrator model that explains both effects with a single mechanism. In this leaky integrator model we introduce the idea that, depending on the task, either the distance from start, or the distance to target is used as a state variable. The state variable is updated during the movement by integration over the space covered by the movement, rather than over time. In this model, travel distance mis-estimation occurs because the integration leaks and because the transformation of visual motion to travel distance involves a gain factor. Mis-estimates in both tasks can be explained with the same leak rate and gain in both conditions. Our results thus suggest that observers do not simply integrate traveled distance and then relate it to the task. Instead, the internally represented variable is either distance from the origin or distance to the goal, whichever is relevant.
Path integral approach to eikonal and next-to-eikonal exponentiation
NASA Astrophysics Data System (ADS)
Laenen, Eric; Stavenga, Gerben; White, Chris D.
2009-03-01
We approach the issue of exponentiation of soft gauge boson corrections to scattering amplitudes from a path integral point of view. We show that if one represents the amplitude as a first quantized path integral in a mixed coordinate-momentum space representation, a charged particle interacting with a soft gauge field is represented as a Wilson line for a semi-infinite line segment, together with calculable fluctuations. Combining such line segments, we show that exponentiation in an abelian field theory follows immediately from standard path-integral combinatorics. In the non-abelian case, we consider color singlet hard interactions with two outgoing external lines, and obtain a new viewpoint for exponentiation in terms of ``webs'', with a closed form solution for their corresponding color factors. We investigate and clarify the structure of next-to-eikonal corrections.
NASA Astrophysics Data System (ADS)
Han, Muxin; Thiemann, T.
2010-11-01
Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. In this paper we review this rather involved procedure in full generality. Moreover, we demonstrate that the reduced phase space path integral formulation formally agrees with the Dirac's operator constraint quantization and, more specifically, with the master constraint quantization for first-class constraints. For first-class constraints with nontrivial structure functions the equivalence can only be established by passing to Abelian(ized) constraints which is always possible locally in phase space. Generically, the correct configuration space path integral measure deviates from the exponential of the Lagrangian action. The corrections are especially severe if the theory suffers from second-class secondary constraints. In a companion paper we compute these corrections for the Holst and Plebanski formulations of GR on which current spin foam models are based.
Robust path integration in the entorhinal grid cell system with hippocampal feed-back.
Samu, Dávid; Eros, Péter; Ujfalussy, Balázs; Kiss, Tamás
2009-07-01
Animals are able to update their knowledge about their current position solely by integrating the speed and the direction of their movement, which is known as path integration. Recent discoveries suggest that grid cells in the medial entorhinal cortex might perform some of the essential underlying computations of path integration. However, a major concern over path integration is that as the measurement of speed and direction is inaccurate, the representation of the position will become increasingly unreliable. In this paper, we study how allothetic inputs can be used to continually correct the accumulating error in the path integrator system. We set up the model of a mobile agent equipped with the entorhinal representation of idiothetic (grid cell) and allothetic (visual cells) information and simulated its place learning in a virtual environment. Due to competitive learning, a robust hippocampal place code emerges rapidly in the model. At the same time, the hippocampo-entorhinal feed-back connections are modified via Hebbian learning in order to allow hippocampal place cells to influence the attractor dynamics in the entorhinal cortex. We show that the continuous feed-back from the integrated hippocampal place representation is able to stabilize the grid cell code.
Pérez, Alejandro; Tuckerman, Mark E
2011-08-14
Higher order factorization schemes are developed for path integral molecular dynamics in order to improve the convergence of estimators for physical observables as a function of the Trotter number. The methods are based on the Takahashi-Imada and Susuki decompositions of the Boltzmann operator. The methods introduced improve the averages of the estimators by using the classical forces needed to carry out the dynamics to construct a posteriori weighting factors for standard path integral molecular dynamics. The new approaches are straightforward to implement in existing path integral codes and carry no significant overhead. The Suzuki higher order factorization was also used to improve the end-to-end distance estimator in open path integral molecular dynamics. The new schemes are tested in various model systems, including an ab initio path integral molecular dynamics calculation on the hydrogen molecule and a quantum water model. The proposed algorithms have potential utility for reducing the cost of path integral molecular dynamics calculations of bulk systems.
NASA Astrophysics Data System (ADS)
Pérez, Alejandro; Tuckerman, Mark E.
2011-08-01
Higher order factorization schemes are developed for path integral molecular dynamics in order to improve the convergence of estimators for physical observables as a function of the Trotter number. The methods are based on the Takahashi-Imada and Susuki decompositions of the Boltzmann operator. The methods introduced improve the averages of the estimators by using the classical forces needed to carry out the dynamics to construct a posteriori weighting factors for standard path integral molecular dynamics. The new approaches are straightforward to implement in existing path integral codes and carry no significant overhead. The Suzuki higher order factorization was also used to improve the end-to-end distance estimator in open path integral molecular dynamics. The new schemes are tested in various model systems, including an ab initio path integral molecular dynamics calculation on the hydrogen molecule and a quantum water model. The proposed algorithms have potential utility for reducing the cost of path integral molecular dynamics calculations of bulk systems.
Path integral measure, constraints and ghosts for massive gravitons with a cosmological constant
Metaxas, Dimitrios
2009-12-15
For massive gravity in a de Sitter background one encounters problems of stability when the curvature is larger than the graviton mass. I analyze this situation from the path integral point of view and show that it is related to the conformal factor problem of Euclidean quantum (massless) gravity. When a constraint for massive gravity is incorporated and the proper treatment of the path integral measure is taken into account one finds that, for particular choices of the DeWitt metric on the space of metrics (in fact, the same choices as in the massless case), one obtains the opposite bound on the graviton mass.
Ab initio path integral ring polymer molecular dynamics: Vibrational spectra of molecules
NASA Astrophysics Data System (ADS)
Shiga, Motoyuki; Nakayama, Akira
2008-01-01
The path integral ring polymer molecular dynamics method is combined with 'on-the-fly' ab initio electronic structure calculations and applied to vibrational spectra of small molecules, LiH and H 2O, at the room temperature. The results are compared with those of the numerically exact solution and ab initio path integral centroid molecular dynamics calculation. The peak positions in the calculated spectra are found to be reasonable, showing the red-shift due to potential anharmonicity. This unification enables the investigation of real-time quantum dynamics of chemically complex molecular systems on the ab initio Born-Oppenheimer potential energy surface.
A path integral approach to asset-liability management
NASA Astrophysics Data System (ADS)
Decamps, Marc; De Schepper, Ann; Goovaerts, Marc
2006-05-01
Functional integrals constitute a powerful tool in the investigation of financial models. In the recent econophysics literature, this technique was successfully used for the pricing of a number of derivative securities. In the present contribution, we introduce this approach to the field of asset-liability management. We work with a representation of cash flows by means of a two-dimensional delta-function perturbation, in the case of a Brownian model and a geometric Brownian model. We derive closed-form solutions for a finite horizon ALM policy. The results are numerically and graphically illustrated.
Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory.
Gao, J
2016-01-01
Path-integral free energy perturbation (PI-FEP) theory is presented to directly determine the ratio of quantum mechanical partition functions of different isotopologs in a single simulation. Furthermore, a double averaging strategy is used to carry out the practical simulation, separating the quantum mechanical path integral exactly into two separate calculations, one corresponding to a classical molecular dynamics simulation of the centroid coordinates, and another involving free-particle path-integral sampling over the classical, centroid positions. An integrated centroid path-integral free energy perturbation and umbrella sampling (PI-FEP/UM, or simply, PI-FEP) method along with bisection sampling was summarized, which provides an accurate and fast convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. The PI-FEP method is illustrated by a number of applications, to highlight the computational precision and accuracy, the rule of geometrical mean in kinetic isotope effects, enhanced nuclear quantum effects in enzyme catalysis, and protein dynamics on temperature dependence of kinetic isotope effects.
A review of path-independent integrals in elastic-plastic fracture mechanics
NASA Technical Reports Server (NTRS)
Kim, Kwang S.; Orange, Thomas W.
1988-01-01
The objective of this paper is to review the path-independent (P-I) integrals in elastic plastic fracture mechanics which have been proposed in recent years to overcome the limitations imposed on the J-integral. The P-I integrals considered are the J-integral by Rice (1968), the thermoelastic P-I integrals by Wilson and Yu (1979) and Gurtin (1979), the J-integral by Blackburn (1972), the J(theta)-integral by Ainsworth et al. (1978), the J-integral by Kishimoto et al. (1980), and the Delta-T(p) and Delta T(p)-asterisk integrals by Alturi et al. (1982). The theoretical foundation of the P-I integrals is examined with an emphasis on whether or not the path independence is maintained in the presence of nonproportional loading and unloading in the plastic regime, thermal gradient, and material inhomogeneities. The simularities, difference, salient features, and limitations of the P-I integrals are discussed. Comments are also made with regard to the physical meaning, the possibility of experimental measurement, and computational aspects.
A review of path-independent integrals in elastic-plastic fracture mechanics, task 4
NASA Technical Reports Server (NTRS)
Kim, K. S.
1985-01-01
The path independent (P-I) integrals in elastic plastic fracture mechanics which have been proposed in recent years to overcome the limitations imposed on the J integral are reviewed. The P-I integrals considered herein are the J integral by Rice, the thermoelastic P-I integrals by Wilson and Yu and by Gurtin, the J* integral by Blackburn, the J sub theta integral by Ainsworth et al., the J integral by Kishimoto et al., and the delta T sub p and delta T* sub p integrals by Atluri et al. The theoretical foundation of these P-I integrals is examined with emphasis on whether or not path independence is maintained in the presence of nonproportional loading and unloading in the plastic regime, thermal gradients, and material inhomogeneities. The similarities, differences, salient features, and limitations of these P-I integrals are discussed. Comments are also made with regard to the physical meaning, the possibility of experimental measurement, and computational aspects.
ERIC Educational Resources Information Center
Fraser, J. Scott; Solovey, Andrew D.; Grove, David; Lee, Mo Yee; Greene, Gilbert J.
2012-01-01
A moderate common factors approach is proposed as a synthesis or middle path to integrate common and specific factors in evidence-based approaches to high-risk youth and families. The debate in family therapy between common and specific factors camps is reviewed and followed by suggestions from the literature for synthesis and creative flexibility…
Singular path-independent energy integrals for elastic bodies with thin elastic inclusions
NASA Astrophysics Data System (ADS)
Shcherbakov, V. V.
2016-06-01
An equilibrium problem for a two-dimensional homogeneous linear elastic body containing a thin elastic inclusion and an interfacial crack is considered. The thin inclusion is modeled within the framework of Euler-Bernoulli beam theory. An explicit formula for the first derivative of the energy functional with respect to the crack perturbation along the interface is presented. It is shown that the formulas for the derivative associated with translation and self-similar expansion of the crack are represented as path-independent integrals along smooth contour surrounding one or both crack tips. These path-independent integrals consist of regular and singular terms and are analogs of the well-known Eshelby-Cherepanov-Rice J-integral and Knowles-Sternberg M-integral.
Factors Affecting Technology Integration in K-12 Classrooms: A Path Model
ERIC Educational Resources Information Center
Inan, Fethi A.; Lowther, Deborah L.
2010-01-01
The purpose of this study was to examine the direct and indirect effects of teachers' individual characteristics and perceptions of environmental factors that influence their technology integration in the classroom. A research-based path model was developed to explain causal relationships between these factors and was tested based on data gathered…
Walters, Peter L; Makri, Nancy
2015-12-17
We employ the quantum-classical path integral methodology to simulate the outer sphere charge-transfer process of the ferrocene-ferrocenium pair in liquid hexane with unprecedented accuracy. Comparison of the simulation results to those obtained by mapping the solvent on an effective harmonic bath demonstrates the accuracy of linear response theory in this system.
Coherent-state path integrals in the continuum: The SU(2) case
NASA Astrophysics Data System (ADS)
Kordas, G.; Kalantzis, D.; Karanikas, A. I.
2016-09-01
We define the time-continuous spin coherent-state path integral in a way that is free from inconsistencies. The proposed definition is used to reproduce known exact results. Such a formalism opens new possibilities for applying approximations with improved accuracy and can be proven useful in a great variety of problems where spin Hamiltonians are used.
Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman Path Integrals Method
ERIC Educational Resources Information Center
Fanaro, Maria de los Angeles; Otero, Maria Rita; Arlego, Marcelo
2012-01-01
This paper discusses the teaching of basic quantum mechanics in high school. Rather than following the usual formalism, our approach is based on Feynman's path integral method. Our presentation makes use of simulation software and avoids sophisticated mathematical formalism. (Contains 3 figures.)
Path-dependent J-integral evaluations around an elliptical hole for large deformation theory
NASA Astrophysics Data System (ADS)
Unger, David J.
2016-08-01
An exact expression is obtained for a path-dependent J-integral for finite strains of an elliptical hole subject to remote tensile tractions under the Tresca deformation theory for a thin plate composed of non-work hardening material. Possible applications include an analytical resistance curve for the initial stage of crack propagation due to crack tip blunting.
Integrated flight path planning system and flight control system for unmanned helicopters.
Jan, Shau Shiun; Lin, Yu Hsiang
2011-01-01
This paper focuses on the design of an integrated navigation and guidance system for unmanned helicopters. The integrated navigation system comprises two systems: the Flight Path Planning System (FPPS) and the Flight Control System (FCS). The FPPS finds the shortest flight path by the A-Star (A*) algorithm in an adaptive manner for different flight conditions, and the FPPS can add a forbidden zone to stop the unmanned helicopter from crossing over into dangerous areas. In this paper, the FPPS computation time is reduced by the multi-resolution scheme, and the flight path quality is improved by the path smoothing methods. Meanwhile, the FCS includes the fuzzy inference systems (FISs) based on the fuzzy logic. By using expert knowledge and experience to train the FIS, the controller can operate the unmanned helicopter without dynamic models. The integrated system of the FPPS and the FCS is aimed at providing navigation and guidance to the mission destination and it is implemented by coupling the flight simulation software, X-Plane, and the computing software, MATLAB. Simulations are performed and shown in real time three-dimensional animations. Finally, the integrated system is demonstrated to work successfully in controlling the unmanned helicopter to operate in various terrains of a digital elevation model (DEM).
Accelerated path integral methods for atomistic simulations at ultra-low temperatures
NASA Astrophysics Data System (ADS)
Uhl, Felix; Marx, Dominik; Ceriotti, Michele
2016-08-01
Path integral methods provide a rigorous and systematically convergent framework to include the quantum mechanical nature of atomic nuclei in the evaluation of the equilibrium properties of molecules, liquids, or solids at finite temperature. Such nuclear quantum effects are often significant for light nuclei already at room temperature, but become crucial at cryogenic temperatures such as those provided by superfluid helium as a solvent. Unfortunately, the cost of converged path integral simulations increases significantly upon lowering the temperature so that the computational burden of simulating matter at the typical superfluid helium temperatures becomes prohibitive. Here we investigate how accelerated path integral techniques based on colored noise generalized Langevin equations, in particular the so-called path integral generalized Langevin equation thermostat (PIGLET) variant, perform in this extreme quantum regime using as an example the quasi-rigid methane molecule and its highly fluxional protonated cousin, CH5+. We show that the PIGLET technique gives a speedup of two orders of magnitude in the evaluation of structural observables and quantum kinetic energy at ultralow temperatures. Moreover, we computed the spatial spread of the quantum nuclei in CH4 to illustrate the limits of using such colored noise thermostats close to the many body quantum ground state.
Accelerated path integral methods for atomistic simulations at ultra-low temperatures.
Uhl, Felix; Marx, Dominik; Ceriotti, Michele
2016-08-07
Path integral methods provide a rigorous and systematically convergent framework to include the quantum mechanical nature of atomic nuclei in the evaluation of the equilibrium properties of molecules, liquids, or solids at finite temperature. Such nuclear quantum effects are often significant for light nuclei already at room temperature, but become crucial at cryogenic temperatures such as those provided by superfluid helium as a solvent. Unfortunately, the cost of converged path integral simulations increases significantly upon lowering the temperature so that the computational burden of simulating matter at the typical superfluid helium temperatures becomes prohibitive. Here we investigate how accelerated path integral techniques based on colored noise generalized Langevin equations, in particular the so-called path integral generalized Langevin equation thermostat (PIGLET) variant, perform in this extreme quantum regime using as an example the quasi-rigid methane molecule and its highly fluxional protonated cousin, CH5 (+). We show that the PIGLET technique gives a speedup of two orders of magnitude in the evaluation of structural observables and quantum kinetic energy at ultralow temperatures. Moreover, we computed the spatial spread of the quantum nuclei in CH4 to illustrate the limits of using such colored noise thermostats close to the many body quantum ground state.
Applications of Path Integral Langevin Dynamics to Weakly Bound Clusters and Biological Molecules
NASA Astrophysics Data System (ADS)
Ing, Christopher; Hinsen, Conrad; Yang, Jing; Roy, Pierre-Nicholas
2011-06-01
We present the use of path integral molecular dynamics (PIMD) in conjunction with the path integral Langevin equation thermostat for sampling systems that exhibit nuclear quantum effects, notably those at low temperatures or those consisting mainly of hydrogen or helium. To test this approach, the internal energy of doped helium clusters are compared with white-noise Langevin thermostatting and high precision path integral monte carlo (PIMC) simulations. We comment on the structural evolution of these clusters in the absence of rotation and exchange as a function of cluster size. To quantify the importance of both rotation and exchange in our PIMD simulation, we compute band origin shifts for (He)_N-CO_2 as a function of cluster size and compare to previously published experimental and theoretical shifts. A convergence study is presented to confirm the systematic error reduction introduced by increasing path integral beads for our implementation in the Molecular Modelling Toolkit (MMTK) software package. Applications to carbohydrates are explored at biological temperatures by calculating both equilibrium and dynamical properties using the methods presented. M. Ceriotti, M. Parrinello, and D. E. Manolopoulos, J Chem Phys 133, 124104. H. Li, N. Blinov, P.-N. Roy, and R. J. L. Roy, J Chem Phys 130, 144305.
PRELIMINARY PROJECT PLAN FOR LANSCE INTEGRATED FLIGHT PATHS 11A, 11B, 12, and 13
D. H. BULTMAN; D. WEINACHT - AIRES CORP.
2000-08-01
This Preliminary Project Plan Summarizes the Technical, Cost, and Schedule baselines for an integrated approach to developing several flight paths at the Manual Lujan Jr. Neutron Scattering Center at the Los Alamos Neutron Science Center. For example, the cost estimate is intended to serve only as a rough order of magnitude assessment of the cost that might be incurred as the flight paths are developed. Further refinement of the requirements and interfaces for each beamline will permit additional refinement and confidence in the accuracy of all three baselines (Technical, Cost, Schedule).
Quantum Mechanics, Path Integrals and Option Pricing:. Reducing the Complexity of Finance
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.; Corianò, Claudio; Srikant, Marakani
2003-04-01
Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some of the methods of lattice simulations of path integrals for the pricing of options. The ideas are sketched out for simple models, such as the Black-Scholes model, where analytical and numerical results are compared. Application of the method to nonlinear systems is also briefly overviewed. More general models, for exotic or path-dependent options are discussed.
Putz, Mihai V.
2009-01-01
The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems. PMID:20087467
Putz, Mihai V
2009-11-10
The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr's quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions - all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.
Tcheang, Lili; Bülthoff, Heinrich H; Burgess, Neil
2011-01-18
Our ability to return to the start of a route recently performed in darkness is thought to reflect path integration of motion-related information. Here we provide evidence that motion-related interoceptive representations (proprioceptive, vestibular, and motor efference copy) combine with visual representations to form a single multimodal representation guiding navigation. We used immersive virtual reality to decouple visual input from motion-related interoception by manipulating the rotation or translation gain of the visual projection. First, participants walked an outbound path with both visual and interoceptive input, and returned to the start in darkness, demonstrating the influences of both visual and interoceptive information in a virtual reality environment. Next, participants adapted to visual rotation gains in the virtual environment, and then performed the path integration task entirely in darkness. Our findings were accurately predicted by a quantitative model in which visual and interoceptive inputs combine into a single multimodal representation guiding navigation, and are incompatible with a model of separate visual and interoceptive influences on action (in which path integration in darkness must rely solely on interoceptive representations). Overall, our findings suggest that a combined multimodal representation guides large-scale navigation, consistent with a role for visual imagery or a cognitive map.
Zhang, Sijie; Schönfeld, Fabian; Wiskott, Laurenz; Manahan-Vaughan, Denise
2014-01-01
Effective spatial navigation is enabled by reliable reference cues that derive from sensory information from the external environment, as well as from internal sources such as the vestibular system. The integration of information from these sources enables dead reckoning in the form of path integration. Navigation in the dark is associated with the accumulation of errors in terms of perception of allocentric position and this may relate to error accumulation in path integration. We assessed this by recording from place cells in the dark under circumstances where spatial sensory cues were suppressed. Spatial information content, spatial coherence, place field size, and peak and infield firing rates decreased whereas sparsity increased following exploration in the dark compared to the light. Nonetheless it was observed that place field stability in darkness was sustained by border information in a subset of place cells. To examine the impact of encountering the environment's border on navigation, we analyzed the trajectory and spiking data gathered during navigation in the dark. Our data suggest that although error accumulation in path integration drives place field drift in darkness, under circumstances where border contact is possible, this information is integrated to enable retention of spatial representations.
Zhang, Sijie; Schönfeld, Fabian; Wiskott, Laurenz; Manahan-Vaughan, Denise
2014-01-01
Effective spatial navigation is enabled by reliable reference cues that derive from sensory information from the external environment, as well as from internal sources such as the vestibular system. The integration of information from these sources enables dead reckoning in the form of path integration. Navigation in the dark is associated with the accumulation of errors in terms of perception of allocentric position and this may relate to error accumulation in path integration. We assessed this by recording from place cells in the dark under circumstances where spatial sensory cues were suppressed. Spatial information content, spatial coherence, place field size, and peak and infield firing rates decreased whereas sparsity increased following exploration in the dark compared to the light. Nonetheless it was observed that place field stability in darkness was sustained by border information in a subset of place cells. To examine the impact of encountering the environment’s border on navigation, we analyzed the trajectory and spiking data gathered during navigation in the dark. Our data suggest that although error accumulation in path integration drives place field drift in darkness, under circumstances where border contact is possible, this information is integrated to enable retention of spatial representations. PMID:25009477
Effective descriptions of complex quantum systems: path integrals and operator ordering problems
NASA Astrophysics Data System (ADS)
Eckern, U.; Gruber, M. J.; Schwab, P.
2005-09-01
[Dedicated to Bernhard Mühlschlegel on the occasion ofhis 80th birthday]We study certain aspects of the effective, occasionally called collective, description of complex quantum systems within the framework of the path integral formalism, in which the environment is integrated out. Generalising the standard Feynman-Vernon Caldeira-Leggett model to include a non-linear coupling between particle and environment, and considering a particular spectral density of the coupling, a coordinate-dependent mass (or velocity-dependent potential) is obtained. The related effective quantum theory, which depends on the proper discretisation of the path integral, is derived and discussed. As a result, we find that in general a simple effective low-energy Hamiltonian, in which only the coordinate-dependent mass enters, cannot be formulated. The quantum theory of weakly coupled superconductors and the quantum dynamics of vortices in Josephson junction arrays are physical examples where these considerations, in principle, are of relevance.
Walters, Daniel; Stringer, Simon; Rolls, Edmund
2013-01-01
The head direction cell system is capable of accurately updating its current representation of head direction in the absence of visual input. This is known as the path integration of head direction. An important question is how the head direction cell system learns to perform accurate path integration of head direction. In this paper we propose a model of velocity path integration of head direction in which the natural time delay of axonal transmission between a linked continuous attractor network and competitive network acts as a timing mechanism to facilitate the correct speed of path integration. The model effectively learns a "look-up" table for the correct speed of path integration. In simulation, we show that the model is able to successfully learn two different speeds of path integration across two different axonal conduction delays, and without the need to alter any other model parameters. An implication of this model is that, by learning look-up tables for each speed of path integration, the model should exhibit a degree of robustness to damage. In simulations, we show that the speed of path integration is not significantly affected by degrading the network through removing a proportion of the cells that signal rotational velocity.
Bressloff, Paul C
2015-01-01
We consider applications of path-integral methods to the analysis of a stochastic hybrid model representing a network of synaptically coupled spiking neuronal populations. The state of each local population is described in terms of two stochastic variables, a continuous synaptic variable and a discrete activity variable. The synaptic variables evolve according to piecewise-deterministic dynamics describing, at the population level, synapses driven by spiking activity. The dynamical equations for the synaptic currents are only valid between jumps in spiking activity, and the latter are described by a jump Markov process whose transition rates depend on the synaptic variables. We assume a separation of time scales between fast spiking dynamics with time constant [Formula: see text] and slower synaptic dynamics with time constant τ. This naturally introduces a small positive parameter [Formula: see text], which can be used to develop various asymptotic expansions of the corresponding path-integral representation of the stochastic dynamics. First, we derive a variational principle for maximum-likelihood paths of escape from a metastable state (large deviations in the small noise limit [Formula: see text]). We then show how the path integral provides an efficient method for obtaining a diffusion approximation of the hybrid system for small ϵ. The resulting Langevin equation can be used to analyze the effects of fluctuations within the basin of attraction of a metastable state, that is, ignoring the effects of large deviations. We illustrate this by using the Langevin approximation to analyze the effects of intrinsic noise on pattern formation in a spatially structured hybrid network. In particular, we show how noise enlarges the parameter regime over which patterns occur, in an analogous fashion to PDEs. Finally, we carry out a [Formula: see text]-loop expansion of the path integral, and use this to derive corrections to voltage-based mean-field equations, analogous
Functional integration of vertical flight path and speed control using energy principles
NASA Technical Reports Server (NTRS)
Lambregts, A. A.
1984-01-01
A generalized automatic flight control system was developed which integrates all longitudinal flight path and speed control functions previously provided by a pitch autopilot and autothrottle. In this design, a net thrust command is computed based on total energy demand arising from both flight path and speed targets. The elevator command is computed based on the energy distribution error between flight path and speed. The engine control is configured to produce the commanded net thrust. The design incorporates control strategies and hierarchy to deal systematically and effectively with all aircraft operational requirements, control nonlinearities, and performance limits. Consistent decoupled maneuver control is achieved for all modes and flight conditions without outer loop gain schedules, control law submodes, or control function duplication.
Color path integral equation of state of the quark-gluon plasma at nonzero chemical potential
NASA Astrophysics Data System (ADS)
Filinov, V. S.; Bonitz, M.; Ivanov, Yu B.; Ilgenfritz, E.-M.; Fortov, V. E.
2015-04-01
Based on the constituent quasiparticle model of the quark-gluon plasma (QGP), a color quantum path-integral Monte-Carlo (PIMC) method for calculation of the thermodynamic properties of the QGP is developed. We show that the PIMC method can be used for calculations of the equation of state at zero and non-zero baryon chemical potential not only above but also below the QCD critical temperature. Our results agree with lattice QCD calculations based on a Taylor expansion around zero baryon chemical potential. In our approach the QGP partition function is presented in the form of a color path integral with a relativistic measure replacing the Gaussian one traditionally used in the Feynman-Wiener path integrals. A procedure of sampling color variables according to the SU(3) group Haar measure is used for integration over the color variables. We expect that this approach will be useful to predict additional properties of the QGP that are still unaccesible in lattice QCD.
The role of spatial memory and frames of reference in the precision of angular path integration.
Arthur, Joeanna C; Philbeck, John W; Kleene, Nicholas J; Chichka, David
2012-09-01
Angular path integration refers to the ability to maintain an estimate of self-location after a rotational displacement by integrating internally-generated (idiothetic) self-motion signals over time. Previous work has found that non-sensory inputs, namely spatial memory, can play a powerful role in angular path integration (Arthur et al., 2007, 2009). Here we investigated the conditions under which spatial memory facilitates angular path integration. We hypothesized that the benefit of spatial memory is particularly likely in spatial updating tasks in which one's self-location estimate is referenced to external space. To test this idea, we administered passive, non-visual body rotations (ranging 40°-140°) about the yaw axis and asked participants to use verbal reports or open-loop manual pointing to indicate the magnitude of the rotation. Prior to some trials, previews of the surrounding environment were given. We found that when participants adopted an egocentric frame of reference, the previously-observed benefit of previews on within-subject response precision was not manifested, regardless of whether remembered spatial frameworks were derived from vision or spatial language. We conclude that the powerful effect of spatial memory is dependent on one's frame of reference during self-motion updating.
The path-independent M Integral around Röthlisberger channels
NASA Astrophysics Data System (ADS)
Meyer, C. R.; Rice, J. R.
2015-12-01
Röthlisberger channels are essential components of subglacial hydrologic systems. Deviations from the Nye creep closure of the ice around a Röthlisberger channel have been long recognized and enhancement factors or a more complex rheology for ice have been suggested as ameliorations to account for channels closing faster than predicted. Here we use the MM integral, a path-independent integral of the equations of continuum mechanics, with a Glen power-law rheology to unify descriptions of creep closure under a variety of stress states surrounding the Röthlisberger channel. The advantage of this approach is that the MM integral around the Röthlisberger channel is equivalent to the integral around the far field. In this way, the creep closure on the channel wall can be determined as a function of the far-field loading, e.g. antiplane shear as well as overburden pressure. We start by analyzing the case of axisymmetric creep closure and we see that the Nye solution is implied by the path-independence of MM integral. We then examine the effects of antiplane shear in several geometries and derive scalings for the creep closure rate based on the MM integral. The results are compared to observations for tunnel closure measurements in a variety of stress states and it is shown that the additional stress components can account for the deviations from the Nye solution. Furthermore, creep closure can be succinctly written in terms of the path-independent MM integral and the variation with applied shear can be found via scalings, which is useful for subglacial hydrology models.
Path-integral and Ornstein-Zernike study of quantum fluid structures on the crystallization line.
Sesé, Luis M
2016-03-07
Liquid neon, liquid para-hydrogen, and the quantum hard-sphere fluid are studied with path integral Monte Carlo simulations and the Ornstein-Zernike pair equation on their respective crystallization lines. The results cover the whole sets of structures in the r-space and the k-space and, for completeness, the internal energies, pressures and isothermal compressibilities. Comparison with experiment is made wherever possible, and the possibilities of establishing k-space criteria for quantum crystallization based on the path-integral centroids are discussed. In this regard, the results show that the centroid structure factor contains two significant parameters related to its main peak features (amplitude and shape) that can be useful to characterize freezing.
Two-scale large deviations for chemical reaction kinetics through second quantization path integral
NASA Astrophysics Data System (ADS)
Li, Tiejun; Lin, Feng
2016-04-01
Motivated by the study of rare events for a typical genetic switching model in systems biology, in this paper we aim to establish the general two-scale large deviations for chemical reaction systems. We build a formal approach to explicitly obtain the large deviation rate functionals for the considered two-scale processes based upon the second quantization path integral technique. We get three important types of large deviation results when the underlying two timescales are in three different regimes. This is realized by singular perturbation analysis to the rate functionals obtained by the path integral. We find that the three regimes possess the same deterministic mean-field limit but completely different chemical Langevin approximations. The obtained results are natural extensions of the classical large volume limit for chemical reactions. We also discuss its implication on the single-molecule Michaelis-Menten kinetics. Our framework and results can be applied to understand general multi-scale systems including diffusion processes.
Proton momentum distribution in water: an open path integral molecular dynamics study.
Morrone, Joseph A; Srinivasan, Varadharajan; Sebastiani, Daniel; Car, Roberto
2007-06-21
Recent neutron Compton scattering experiments have detected the proton momentum distribution in water. The theoretical calculation of this property can be carried out via "open" path integral expressions. In this work, present an extension of the staging path integral molecular dynamics method, which is then employed to calculate the proton momentum distributions of water in the solid, liquid, and supercritical phases. We utilize a flexible, single point charge empirical force field to model the system's interactions. The calculated momentum distributions depict both agreement and discrepancies with experiment. The differences may be explained by the deviation of the force field from the true interactions. These distributions provide an abundance of information about the environment and interactions surrounding the proton.
Moran, B.; Kulkarni, S.S.; Reeves, H.W.
2007-01-01
A path-independent (conservation) integral is developed for the characterization of solute concentration and flux in a biofilm in the vicinity of a detachment or other flux limiting boundary condition. Steady state conditions of solute diffusion are considered and biofilm kinetics are described by an uptake term which can be expressed in terms of a potential (Michaelis-Menten kinetics). An asymptotic solution for solute concentration at the tip of the detachment is obtained and shown to be analogous to that of antiplane crack problems in linear elasticity. It is shown that the amplitude of the asymptotic solution can be calculated by evaluating a path-independent integral. The special case of a semi-infinite detachment in an infinite strip is considered and the amplitude of the asymptotic field is related to the boundary conditions and problem parameters in closed form for zeroth and first order kinetics and numerically for Michaelis-Menten kinetics. ?? Springer Science+Business Media, Inc. 2007.
From path integrals to tensor networks for the AdS /CFT correspondence
NASA Astrophysics Data System (ADS)
Miyaji, Masamichi; Takayanagi, Tadashi; Watanabe, Kento
2017-03-01
In this paper, we discuss tensor network descriptions of AdS /CFT from two different viewpoints. First, we start with a Euclidean path-integral computation of ground state wave functions with a UV cutoff. We consider its efficient optimization by making its UV cutoff position dependent and define a quantum state at each length scale. We conjecture that this path integral corresponds to a time slice of anti-de Sitter (AdS) spacetime. Next, we derive a flow of quantum states by rewriting the action of Killing vectors of AdS3 in terms of the dual two-dimensional conformal field theory (CFT). Both approaches support a correspondence between the hyperbolic time slice H2 in AdS3 and a version of continuous multiscale entanglement renormalization ansatz. We also give a heuristic argument about why we can expect a sub-AdS scale bulk locality for holographic CFTs.
Efficient algorithms for semiclassical instanton calculations based on discretized path integrals
Kawatsu, Tsutomu E-mail: smiura@mail.kanazawa-u.ac.jp; Miura, Shinichi E-mail: smiura@mail.kanazawa-u.ac.jp
2014-07-14
Path integral instanton method is a promising way to calculate the tunneling splitting of energies for degenerated two state systems. In order to calculate the tunneling splitting, we need to take the zero temperature limit, or the limit of infinite imaginary time duration. In the method developed by Richardson and Althorpe [J. Chem. Phys. 134, 054109 (2011)], the limit is simply replaced by the sufficiently long imaginary time. In the present study, we have developed a new formula of the tunneling splitting based on the discretized path integrals to take the limit analytically. We have applied our new formula to model systems, and found that this approach can significantly reduce the computational cost and gain the numerical accuracy. We then developed the method combined with the electronic structure calculations to obtain the accurate interatomic potential on the fly. We present an application of our ab initio instanton method to the ammonia umbrella flip motion.
Path integral methods for the dynamics of stochastic and disordered systems
NASA Astrophysics Data System (ADS)
Hertz, John A.; Roudi, Yasser; Sollich, Peter
2017-01-01
We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin-Siggia-Rose/Janssen-De Dominicis-Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey of the perturbative, i.e. diagrammatic, approach to dynamics and how this formalism can be used for studying soft spin models. We review the supersymmetric formulation of the Langevin dynamics of these models and discuss the physical implications of the supersymmetry. We also describe the key steps involved in studying the disorder-averaged dynamics. Finally, we discuss the path integral approach for the case of hard Ising spins and review some recent developments in the dynamics of such kinetic Ising models.
Path integral investigation of the electronic spectra of He-tetracene clusters
NASA Astrophysics Data System (ADS)
Whitley, Heather D.; Whaley, K. Birgitta
2008-03-01
Planar aromatic molecules (PAMs) are nanoscale precursors to bulk graphite. Their electronic spectra have been extensively studied in ^4He nanodroplets and show a number of unusual spectroscopic features. We have conducted many-body quantum simulations of tetracene in He nanodroplets to probe the 1.1 cm-1 spectral splitting of the electronic origin seen for this PAM. We calculate spectral shifts and He density profiles via path integral quantum Monte Carlo simulations. The spectral splitting is examined using a path integral correlation function approach to determine the lowest-lying vibrational excitation frequencies for small HeN-tetracene clusters. Simulations in the S1 state of tetracene utilize a semi-empirical perturbative interaction potential for a He atom with a PAM. Results for the splitting of the electronic origin and the spectral shifts are in good agreement with experiment. Prepared by LLNL under Contract DE-AC52-07NA27344.
Proton momentum distributions in water: A path integral molecular dynamics study
NASA Astrophysics Data System (ADS)
Srinivasan, Varadharajan; Morrone, Joseph A.; Sebastiani, Daniel; Car, Roberto
2007-03-01
Recent neutron Compton scattering experiments have detected the proton momentum distributions of water. This density in momentum space is a quantum mechanical property of the proton, due to the confining anharmonic potential from covalent and hydrogen bonds. The theoretical calculation of this property can be carried out via ``open'' path integral expressions. In this work, we present an extension of the staging path integral molecular dynamics method, which is then employed to calculate the proton momentum distributions of water in the solid, liquid, and supercritical phases. We utilize the SPC/F2 empirical force field to model the system's interactions. The calculated momentum distributions depict both agreement and discrepancies with experiment. The differences may be explained by the deviation of the force field from the true interactions. These distributions provide an abundance of information about the environment and interactions surrounding the proton.
Proton momentum distribution in water: an open path integral molecular dynamics study
NASA Astrophysics Data System (ADS)
Morrone, Joseph A.; Srinivasan, Varadharajan; Sebastiani, Daniel; Car, Roberto
2007-06-01
Recent neutron Compton scattering experiments have detected the proton momentum distribution in water. The theoretical calculation of this property can be carried out via "open" path integral expressions. In this work, present an extension of the staging path integral molecular dynamics method, which is then employed to calculate the proton momentum distributions of water in the solid, liquid, and supercritical phases. We utilize a flexible, single point charge empirical force field to model the system's interactions. The calculated momentum distributions depict both agreement and discrepancies with experiment. The differences may be explained by the deviation of the force field from the true interactions. These distributions provide an abundance of information about the environment and interactions surrounding the proton.
Simulations of one- and two-electron systems by Bead-Fourier path integral molecular dynamics
NASA Astrophysics Data System (ADS)
Ivanov, Sergei D.; Lyubartsev, Alexander P.
2005-07-01
The Bead-Fourier path integral molecular dynamics technique introduced earlier [S. D. Ivanov, A. P. Lyubartsev, and A. Laaksonen, Phys. Rev. E 67 066710 (2003)] is applied for simulation of electrons in the simplest molecules: molecular hydrogen, helium atom, and their ions. Special attention is paid to the correct description of electrons in the core region of a nucleus. In an attempt to smooth the Coulomb potential at small distances, a recipe is suggested. The simulation results are in excellent agreement with the analytical solution for the "harmonic helium atom", as well as with the vibrational potential of the H2 molecule and He ionization energies. It is demonstrated, that the Bead-Fourier path integral molecular dynamics technique is able to provide the accuracy required for the description of electron structure and chemical bonds in cases when electron exchange effects need not be taken into account.
Ab Initio Path Integral Molecular Dynamics Simulation of Hydrogen in Silicon
NASA Astrophysics Data System (ADS)
Probert, M. I. J.; Glover, M. J.
2006-05-01
We report results of a first-principles theoretical study of an isolated neutral hydrogen atom in crystalline silicon. Spin-polarised density functional theory is used to treat the electrons, and the path-integral molecular dynamics method is used to describe the quantum properties of the nucleus at finite temperature. This is necessary as the hydrogen atom has sufficiently low mass that it exhibits significant nuclear quantum delocalisation and zero-point motion even at room temperature. Unlike post-hoc treatments, such as calculating a static potential energy surface, the path-integral treatment enables such effects to be included "on-the-fly". This is found to be significant, as a coupling is found between the structure of the host silicon lattice and the quantum delocalisation of the hydrogen defect.
A unified scheme for ab initio molecular orbital theory and path integral molecular dynamics
NASA Astrophysics Data System (ADS)
Shiga, Motoyuki; Tachikawa, Masanori; Miura, Shinichi
2001-11-01
We present a general approach for accurate calculation of chemical substances which treats both nuclei and electrons quantum mechanically, adopting ab initio molecular orbital theory for the electronic structure and path integral molecular dynamics for the nuclei. The present approach enables the evaluation of physical quantities dependent on the nuclear configuration as well as the electronic structure, within the framework of Born-Oppenheimer adiabatic approximation. As an application, we give the path integral formulation of electric response properties—dipole moment and polarizability, which characterize the changes both in electronic structure and nuclear configuration at a given temperature when uniform electrostatic field is present. We also demonstrate the calculation of a water molecule using the present approach and the result of temperature and isotope effects is discussed.
Path integral formalism for the spectral line shape in plasmas: Lyman-{alpha} with fine structure
Bedida, N.; Meftah, M. T.; Boland, D.; Stamm, R.
2008-10-22
We examine in this work the expression of the dipolar autocorrelation function for an emitter in the plasma using the path integrals formalism. The results for Lyman alpha lines with fine structure are retrieved in a compact formula. The expression of the dipolar autocorrelation function takes into account the ions dynamics and the fine structure effects. The electron's effect is represented by the impact operator {phi}{sub e} in the final formula.
Path-integral simulations of zero-point effects for implanted muons in benzene
NASA Astrophysics Data System (ADS)
Valladares, R. M.; Fisher, A. J.; Hayes, W.
1995-08-01
We describe a simulation method which is capable of treating the quantum fluctuations of an implanted muon and the electronic structure of the system simultaneously. The partition function for the muon is evaluated using a discretized imaginary-time path-integral technique, using electronic energies and forces evaluated from a semi-empirical quantum chemical treatment of the electronic structure. An application to the cyclohexadienyl radical (C 6H 7) and its muonated analogue (C 6H 6Mu) is presented.
NASA Technical Reports Server (NTRS)
Yu, Jirong; Petros, Mulugeta; Reithmaier, Karl; Bai, Yingxin; Trieu, Bo C.; Refaat, Tamer F.; Kavaya, Michael J.; Singh, Upendra N.
2012-01-01
A 2-micron pulsed, Integrated Path Differential Absorption (IPDA) lidar instrument for ground and airborne atmospheric CO2 concentration measurements via direct detection method is being developed at NASA Langley Research Center. This instrument will provide an alternate approach to measure atmospheric CO2 concentrations with significant advantages. A high energy pulsed approach provides high-precision measurement capability by having high signal-to-noise level and unambiguously eliminates the contamination from aerosols and clouds that can bias the IPDA measurement.
Path integral solution for a deformed radial Rosen-Morse potential
NASA Astrophysics Data System (ADS)
Kadja, A.; Benamira, F.; Guechi, L.
2017-03-01
An exact path integral treatment of a particle in a deformed radial Rosen-Morse potential is presented. For this problem with the Dirichlet boundary conditions, the Green's function is constructed in a closed form by adding to Vq(r) a δ-function perturbation and making its strength infinitely repulsive. A transcendental equation for the energy levels E_{nr} and the wave functions of the bound states can then be deduced.
Phase space path-integral formulation of the above-threshold ionization
NASA Astrophysics Data System (ADS)
Milošević, D. B.
2013-04-01
Atoms and molecules submitted to a strong laser field can emit electrons of high energies in the above-threshold ionization (ATI) process. This process finds a highly intuitive and also quantitative explanation in terms of Feynman's path integral and the concept of quantum orbits [P. Salières et al., Science 292, 902 (2001)], 10.1126/science.108836. However, the connection with the Feynman path-integral formalism is explained only by intuition and analogy and within the so-called strong-field approximation (SFA). Using the phase space path-integral formalism we have obtained an exact result for the momentum-space matrix element of the total time-evolution operator. Applying this result to the ATI we show that the SFA and the so-called improved SFA are, respectively, the zeroth- and the first-order terms of the expansion in powers of the laser-free effective interaction of the electron with the rest of the atom (molecule). We have also presented the second-order term of this expansion which is responsible for the ATI with double scattering of the ionized electron.
Dornheim, Tobias; Schoof, Tim; Groth, Simon; Filinov, Alexey; Bonitz, Michael
2015-11-28
The uniform electron gas (UEG) at finite temperature is of high current interest due to its key relevance for many applications including dense plasmas and laser excited solids. In particular, density functional theory heavily relies on accurate thermodynamic data for the UEG. Until recently, the only existing first-principle results had been obtained for N = 33 electrons with restricted path integral Monte Carlo (RPIMC), for low to moderate density, rs=r¯/aB≳1. These data have been complemented by configuration path integral Monte Carlo (CPIMC) simulations for rs ≤ 1 that substantially deviate from RPIMC towards smaller rs and low temperature. In this work, we present results from an independent third method-the recently developed permutation blocking path integral Monte Carlo (PB-PIMC) approach [T. Dornheim et al., New J. Phys. 17, 073017 (2015)] which we extend to the UEG. Interestingly, PB-PIMC allows us to perform simulations over the entire density range down to half the Fermi temperature (θ = kBT/EF = 0.5) and, therefore, to compare our results to both aforementioned methods. While we find excellent agreement with CPIMC, where results are available, we observe deviations from RPIMC that are beyond the statistical errors and increase with density.
Calculation of heat capacities of light and heavy water by path-integral molecular dynamics
NASA Astrophysics Data System (ADS)
Shiga, Motoyuki; Shinoda, Wataru
2005-10-01
As an application of atomistic simulation methods to heat capacities, path-integral molecular dynamics has been used to calculate the constant-volume heat capacities of light and heavy water in the gas, liquid, and solid phases. While the classical simulation based on conventional molecular dynamics has estimated the heat capacities too high, the quantum simulation based on path-integral molecular dynamics has given reasonable results based on the simple point-charge/flexible potential model. The calculated heat capacities (divided by the Boltzmann constant) in the quantum simulation are 3.1 in the vapor H2O at 300 K, 6.9 in the liquid H2O at 300 K, and 4.1 in the ice IhH2O at 250 K, respectively, which are comparable to the experimental data of 3.04, 8.9, and 4.1, respectively. The quantum simulation also reproduces the isotope effect. The heat capacity in the liquid D2O has been calculated to be 10% higher than that of H2O, while it is 13% higher in the experiment. The results demonstrate that the path-integral simulation is a promising approach to quantitatively evaluate the heat capacities for molecular systems, taking account of quantum-mechanical vibrations as well as strongly anharmonic motions.
i-PI: A Python interface for ab initio path integral molecular dynamics simulations
NASA Astrophysics Data System (ADS)
Ceriotti, Michele; More, Joshua; Manolopoulos, David E.
2014-03-01
Recent developments in path integral methodology have significantly reduced the computational expense of including quantum mechanical effects in the nuclear motion in ab initio molecular dynamics simulations. However, the implementation of these developments requires a considerable programming effort, which has hindered their adoption. Here we describe i-PI, an interface written in Python that has been designed to minimise the effort required to bring state-of-the-art path integral techniques to an electronic structure program. While it is best suited to first principles calculations and path integral molecular dynamics, i-PI can also be used to perform classical molecular dynamics simulations, and can just as easily be interfaced with an empirical forcefield code. To give just one example of the many potential applications of the interface, we use it in conjunction with the CP2K electronic structure package to showcase the importance of nuclear quantum effects in high-pressure water. Catalogue identifier: AERN_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AERN_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 138626 No. of bytes in distributed program, including test data, etc.: 3128618 Distribution format: tar.gz Programming language: Python. Computer: Multiple architectures. Operating system: Linux, Mac OSX, Windows. RAM: Less than 256 Mb Classification: 7.7. External routines: NumPy Nature of problem: Bringing the latest developments in the modelling of nuclear quantum effects with path integral molecular dynamics to ab initio electronic structure programs with minimal implementational effort. Solution method: State-of-the-art path integral molecular dynamics techniques are implemented in a Python interface. Any electronic structure code can be patched to receive the atomic
Treatment of the hydrogen atom in an electric field by the path-integral formalism
Chetouani, L.; Hammann, T.F.
1986-12-01
The Feynman path-integral method is applied to solve the problem of a H atom in an electric field. In accordance with the midpoint philosophy, the propagators are symmetrized in every time interval and, via several transformations, one of which is the Langer modification, the Green's function is calculated in parabolic coordinates, decomposed into partial propagators, and expressed in terms of two one-dimensional Green's functions. The perturbation method being no more valid for high excited levels, the spectrum is given, according to the WKB method, as a solution of a system of two elliptic integral equations. The exact spectrum of the H atom is obtained for a zero electric field.
NASA Astrophysics Data System (ADS)
Imaoka, Haruna; Kinugawa, Kenichi
2017-03-01
Thermal conductivity, shear viscosity, and bulk viscosity of normal liquid 4He at 1.7-4.0 K are calculated using path integral centroid molecular dynamics (CMD) simulations. The calculated thermal conductivity and shear viscosity above lambda transition temperature are on the same order of magnitude as experimental values, while the agreement of shear viscosity is better. Above 2.3 K the CMD well reproduces the temperature dependences of isochoric shear viscosity and of the time integral of the energy current and off-diagonal stress tensor correlation functions. The calculated bulk viscosity, not known in experiments, is several times larger than shear viscosity.
NASA Astrophysics Data System (ADS)
Han, Muxin
2010-12-01
This paper serves as a continuation for the discussion in Engle et al (2010, Class. Quantum Grav. 27 245014). We analyze the invariance properties of the gravity path-integral measure derived from canonical framework and discuss which path-integral formula may be employed in the concrete computation e.g. constructing a spin-foam model, so that the final model can be interpreted as a physical inner product in the canonical theory. This paper is divided into two parts, the first part is concerning the gauge invariance of the canonical path-integral measure for gravity from the reduced phase space quantization. We show that the path-integral measure is invariant under all the gauge transformations generated by all the constraints. These gauge transformations are the local symmetries of the gravity action, which is implemented without anomaly at the quantum level by the invariant path-integral measure. However, these gauge transformations coincide with the spacetime diffeomorphisms only when the equations of motion are imposed. But the path-integral measure is not invariant under spacetime diffeomorphisms, i.e. the local symmetry of spacetime diffeomorphisms become anomalous in the reduced phase space path-integral quantization. In the second part, we present a path-integral formula, which formally solves all the quantum constraint equations of gravity, and further results in a rigging map in the sense of refined algebraic quantization (RAQ). Then we give a formal path-integral expression of the physical inner product in loop quantum gravity (LQG). This path-integral expression is simpler than the one from reduced phase space quantization, since all the gauge-fixing conditions are removed except the time gauge. The resulting path-integral measure is different from the product Lebesgue measure up to a local measure factor containing both the spacetime volume element and the spatial volume element. This formal path-integral expression of the physical inner product can be
Accurate path integration in continuous attractor network models of grid cells.
Burak, Yoram; Fiete, Ila R
2009-02-01
Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of approximately 10-100 meters and approximately 1-10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.
Yang, Sandy; Yamamoto, Takeshi; Miller, William H.
2005-11-28
The quantum instanton approximation is a type of quantum transition state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low order derivatives at time zero. Here we present several path-integral estimators for the latter quantities, which characterize the initial decay profile of the flux correlation function. As with the internal energy or heat capacity calculation, different estimators yield different variances (and therefore different convergence properties) in a Monte Carlo calculation. Here we obtain a virial(-type) estimator by using a coordinate scaling procedure rather than integration by parts, which allows more computational benefits. We also consider two different methods for treating the flux operator, i.e., local-path and global-path approaches, in which the latter achieves a smaller variance at the cost of using second-order potential derivatives. Numerical tests are performed for a one-dimensional Eckart barrier and a model proton transfer reaction in a polar solvent, which illustrates the reduced variance of the virial estimator over the corresponding thermodynamic estimator.
Israël, I; Grasso, R; Georges-Francois, P; Tsuzuku, T; Berthoz, A
1997-06-01
According to path integration, the brain is able to compute the distance of a traveled path. In this research we applied our previously reported method for studying memory of linear distance, a crucial mechanism in path integration; our method is based on the overt reconstruction of a passive transport. Passive transport is a special case of navigation in which no active control is performed. Blindfolded subjects were first asked to travel 2 m forward, in darkness, by driving with a joystick the robot on which they were seated. The results show that all subjects but two undershot this distance, i.e., overestimated their own displacement. Then, subjects were submitted to a passive linear forward displacement along 2, 4, 6, 8, or 10 m, and had to reproduce the same distance, still blindfolded. The results show that the distance of the stimulus was accurately reproduced, as well as stimulus duration, peak velocity, and velocity profile. In this first condition, the imposed velocity profile was triangular and therefore stimulus distance and duration were correlated. In a second condition, it was shown that distance was correctly reproduced also when the information about stimulus duration was kept constant. Here, different velocity profiles were used as stimuli, and most subjects also reproduced the velocity profile. Statistical analyses indicated that distance was not reproduced as a consequence of duration, peak velocity, or velocity profile reproduction, but was uniquely correlated to stimulus distance. The previous hypothesis of a double integration of the otolith signal to provide a distance estimate can explain our results. There was a large discrepancy between the accuracy with which the subjects matched the velocity profiles and that of distance reproduction. It follows that, whereas the dynamics of passive motion are stored and available to further use, distance is independently estimated. It is concluded that vestibular and somatosensory signals excited by
Dynamic response characteristics of dual flow-path integrally bladed rotors
NASA Astrophysics Data System (ADS)
Beck, Joseph A.; Brown, Jeffrey M.; Scott-Emuakpor, Onome E.; Cross, Charles J.; Slater, Joseph C.
2015-02-01
New turbine engine designs requiring secondary flow compression often look to dual flow-path integrally bladed rotors (DFIBRs) since these stages have the ability to perform work on the secondary, or bypassed, flow-field. While analogous to traditional integrally bladed rotor stages, DFIBR designs have many differences that result in unique dynamic response characteristics that must be understood to avoid fatigue. This work investigates these characteristics using reduced-order models (ROMs) that incorporate mistuning through perturbations to blade frequencies. This work provides an alternative to computationally intensive geometric-mistuning approaches for DFIBRs by utilizing tuned blade mode reductions and substructure coupling in cyclic coordinates. Free and forced response results are compared to full finite element model (FEM) solutions to determine if any errors are related to the reduced-order model formulation reduction methods. It is shown that DFIBRs have many more frequency veering regions than their single flow-path integrally blade rotor (IBR) counterparts. Modal families are shown to transition between system, inner-blade, and outer-blade motion. Furthermore, findings illustrate that while mode localization of traditional IBRs is limited to a single or small subset of blades, DFIBRs can have modal energy localized to either an inner- or outer-blade set resulting in many blades responding above tuned levels. Lastly, ROM forced response predictions compare well to full FEM predictions for the two test cases shown.
NASA Astrophysics Data System (ADS)
Yamamoto, Takeshi; Miller, William H.
2005-01-01
The quantum instanton approximation for thermal rate constants, a type of quantum transition state theory (QTST), is applied to a model proton transfer reaction in liquid methyl chloride developed by Azzouz and Borgis. Monte Carlo path integral methods are used to carry out the calculations, and two other closely related QTST's, namely, the centroid-density and Hansen-Andersen QTST, are also evaluated for comparison using the present path integral approach. A technique is then introduced that calculates the kinetic isotope effect directly via thermodynamic integration of the rate with respect to hydrogen mass, which has the practical advantage of avoiding costly evaluation of the activation free energy. The present application to the Azzouz-Borgis problem shows that the above three types of QTST provide very similar results for the rate, within 30% of each other, which is nontrivial considering the totally different derivations of these QTSTs; the latter rates are also in reasonable agreement with some other previous results (e.g., obtained via molecular dynamics with quantum transitions), within a factor of ˜2(7) for the H(D) transfer, thus significantly diminishing the possible range of the exact rates. In addition, it is revealed that a small but nonnegligible inconsistency exists in the parametrization of the Azzouz-Borgis model employed in previous studies, which resulted in the large apparent discrepancy in the calculated rates.
Geng, Hua Y.
2015-02-15
A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics (AI-PIMD) simulation, without compromising the overall accuracy. To validate the method, the internal energy and free energy of an Einstein crystal are calculated and compared with the analytical solutions. As a preliminary application, we assess the performance of the method in a realistic model—the FCC phase of dense atomic hydrogen, in which the calculated result shows that the acceleration rate is about 3 to 4-fold for a two-level implementation, and can be increased up to 10 times if extrapolation is used. With only 16 beads used for the ab initio potential sampling, this method gives a well converged internal energy. The residual error in pressure is just about 3 GPa, whereas it is about 20 GPa for a plain AI-PIMD calculation with the same number of beads. The vibrational free energy of the FCC phase of dense hydrogen at 300 K is also calculated with an AI-PIMD thermodynamic integration method, which gives a result of about 0.51 eV/proton at a density of r{sub s}=0.912.
NASA Astrophysics Data System (ADS)
Minary, Peter; Martyna, Glenn J.; Tuckerman, Mark E.
2003-02-01
In this paper (Paper I) and a companion paper (Paper II), novel new algorithms and applications of the isokinetic ensemble as generated by Gauss' principle of least constraint, pioneered for use with molecular dynamics 20 years ago, are presented for biophysical, path integral, and Car-Parrinello based ab initio molecular dynamics. In Paper I, a new "extended system" version of the isokinetic equations of motion that overcomes the ergodicity problems inherent in the standard approach, is developed using a new theory of non-Hamiltonian phase space analysis [M. E. Tuckerman et al., Europhys. Lett. 45, 149 (1999); J. Chem. Phys. 115, 1678 (2001)]. Reversible multiple time step integrations schemes for the isokinetic methods, first presented by Zhang [J. Chem. Phys. 106, 6102 (1997)] are reviewed. Next, holonomic constraints are incorporated into the isokinetic methodology for use in fast efficient biomolecular simulation studies. Model and realistic examples are presented in order to evaluate, critically, the performance of the new isokinetic molecular dynamic schemes. Comparisons are made to the, now standard, canonical dynamics method, Nosé-Hoover chain dynamics [G. J. Martyna et al., J. Chem. Phys. 97, 2635 (1992)]. The new isokinetic techniques are found to yield more efficient sampling than the Nosé-Hoover chain method in both path integral molecular dynamics and biophysical molecular dynamics calculations. In Paper II, the use of isokinetic methods in Car-Parrinello based ab initio molecular dynamics calculations is presented.
NASA Astrophysics Data System (ADS)
Geng, Hua Y.
2015-02-01
A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics (AI-PIMD) simulation, without compromising the overall accuracy. To validate the method, the internal energy and free energy of an Einstein crystal are calculated and compared with the analytical solutions. As a preliminary application, we assess the performance of the method in a realistic model-the FCC phase of dense atomic hydrogen, in which the calculated result shows that the acceleration rate is about 3 to 4-fold for a two-level implementation, and can be increased up to 10 times if extrapolation is used. With only 16 beads used for the ab initio potential sampling, this method gives a well converged internal energy. The residual error in pressure is just about 3 GPa, whereas it is about 20 GPa for a plain AI-PIMD calculation with the same number of beads. The vibrational free energy of the FCC phase of dense hydrogen at 300 K is also calculated with an AI-PIMD thermodynamic integration method, which gives a result of about 0.51 eV/proton at a density of rs = 0.912.
Error Reduction Methods for Integrated-path Differential-absorption Lidar Measurements
NASA Technical Reports Server (NTRS)
Chen, Jeffrey R.; Numata, Kenji; Wu, Stewart T.
2012-01-01
We report new modeling and error reduction methods for differential-absorption optical-depth (DAOD) measurements of atmospheric constituents using direct-detection integrated-path differential-absorption lidars. Errors from laser frequency noise are quantified in terms of the line center fluctuation and spectral line shape of the laser pulses, revealing relationships verified experimentally. A significant DAOD bias is removed by introducing a correction factor. Errors from surface height and reflectance variations can be reduced to tolerable levels by incorporating altimetry knowledge and "log after averaging", or by pointing the laser and receiver to a fixed surface spot during each wavelength cycle to shorten the time of "averaging before log".
NASA Astrophysics Data System (ADS)
Artoun, Ojenie; David-Rus, Diana; Emmett, Matthew; Fishman, Lou; Fital, Sandra; Hogan, Chad; Lim, Jisun; Lushi, Enkeleida; Marinov, Vesselin
2006-05-01
In this report we summarize an extension of Fourier analysis for the solution of the wave equation with a non-constant coefficient corresponding to an inhomogeneous medium. The underlying physics of the problem is exploited to link pseudodifferential operators and phase space path integrals to obtain a marching algorithm that incorporates the backward scattering into the evolution of the wave. This allows us to successfully apply single-sweep, one-way marching methods in inherently two-way environments, which was not achieved before through other methods for this problem.
Temperature-dependent isovector pairing gap equations using a path integral approach
Fellah, M.; Allal, N. H.; Belabbas, M.; Oudih, M. R.; Benhamouda, N.
2007-10-15
Temperature-dependent isovector neutron-proton (np) pairing gap equations have been established by means of the path integral approach. These equations generalize the BCS ones for the pairing between like particles at finite temperature. The method has been numerically tested using the one-level model. It has been shown that the gap parameter {delta}{sub np} has a behavior analogous to that of {delta}{sub nn} and {delta}{sub pp} as a function of the temperature: one notes the presence of a critical temperature. Moreover, it has been shown that the isovector pairing effects remain beyond the critical temperature that corresponds to the pairing between like particles.
Path-integral calculation of the third virial coefficient of quantum gases at low temperatures
Garberoglio, Giovanni; Harvey, Allan H.
2011-04-07
We derive path-integral expressions for the second and third virial coefficients of monatomic quantum gases. Unlike previous work that considered only Boltzmann statistics, we include exchange effects (Bose-Einstein or Fermi-Dirac statistics). We use state-of-the-art pair and three-body potentials to calculate the third virial coefficient of {sup 3}He and {sup 4}He in the temperature range 2.6-24.5561 K. We obtain uncertainties smaller than those of the limited experimental data. Inclusion of exchange effects is necessary to obtain accurate results below about 7 K.
Path-integral calculation of the third virial coefficient of quantum gases at low temperatures.
Garberoglio, Giovanni; Harvey, Allan H
2011-04-07
We derive path-integral expressions for the second and third virial coefficients of monatomic quantum gases. Unlike previous work that considered only Boltzmann statistics, we include exchange effects (Bose-Einstein or Fermi-Dirac statistics). We use state-of-the-art pair and three-body potentials to calculate the third virial coefficient of (3)He and (4)He in the temperature range 2.6-24.5561 K. We obtain uncertainties smaller than those of the limited experimental data. Inclusion of exchange effects is necessary to obtain accurate results below about 7 K.
NASA Astrophysics Data System (ADS)
Garberoglio, Giovanni; Jankowski, Piotr; Szalewicz, Krzysztof; Harvey, Allan H.
2014-07-01
We present a path-integral Monte Carlo procedure for the fully quantum calculation of the second molecular virial coefficient accounting for intramolecular flexibility. This method is applied to molecular hydrogen (H2) and deuterium (D2) in the temperature range 15-2000 K, showing that the effect of molecular flexibility is not negligible. Our results are in good agreement with experimental data, as well as with virials given by recent empirical equations of state, although some discrepancies are observed for H2 between 100 and 200 K.
Garberoglio, Giovanni; Jankowski, Piotr; Szalewicz, Krzysztof; Harvey, Allan H
2014-07-28
We present a path-integral Monte Carlo procedure for the fully quantum calculation of the second molecular virial coefficient accounting for intramolecular flexibility. This method is applied to molecular hydrogen (H2) and deuterium (D2) in the temperature range 15-2000 K, showing that the effect of molecular flexibility is not negligible. Our results are in good agreement with experimental data, as well as with virials given by recent empirical equations of state, although some discrepancies are observed for H2 between 100 and 200 K.
Path integral representation of spin foam models of 4D gravity
NASA Astrophysics Data System (ADS)
Conrady, Florian; Freidel, Laurent
2008-12-01
We give a unified description of all recent spin foam models introduced by Engle, Livine, Pereira and Rovelli (ELPR) and by Freidel and Krasnov (FK). We show that the FK models are, for all values of the Immirzi parameter γ, equivalent to path integrals of a discrete theory and we provide an explicit formula for the associated actions. We discuss the relation between the FK and ELPR models and also study the corresponding boundary states. For general Immirzi parameter, these are given by Alexandrov's and Livine's SO(4) projected states. For 0 <= γ < 1, the states can be restricted to SU(2) spin networks.
An introduction to stochastic control theory, path integrals and reinforcement learning
NASA Astrophysics Data System (ADS)
Kappen, Hilbert J.
2007-02-01
Control theory is a mathematical description of how to act optimally to gain future rewards. In this paper I give an introduction to deterministic and stochastic control theory and I give an overview of the possible application of control theory to the modeling of animal behavior and learning. I discuss a class of non-linear stochastic control problems that can be efficiently solved using a path integral or by MC sampling. In this control formalism the central concept of cost-to-go becomes a free energy and methods and concepts from statistical physics can be readily applied.
Liu, Jian; Zhang, Zhijun
2016-01-21
Path integral Liouville dynamics (PILD) is applied to vibrational dynamics of several simple but representative realistic molecular systems (OH, water, ammonia, and methane). The dipole-derivative autocorrelation function is employed to obtain the infrared spectrum as a function of temperature and isotopic substitution. Comparison to the exact vibrational frequency shows that PILD produces a reasonably accurate peak position with a relatively small full width at half maximum. PILD offers a potentially useful trajectory-based quantum dynamics approach to compute vibrational spectra of molecular systems.
Garberoglio, Giovanni; Jankowski, Piotr; Szalewicz, Krzysztof; Harvey, Allan H.
2014-07-28
We present a path-integral Monte Carlo procedure for the fully quantum calculation of the second molecular virial coefficient accounting for intramolecular flexibility. This method is applied to molecular hydrogen (H{sub 2}) and deuterium (D{sub 2}) in the temperature range 15–2000 K, showing that the effect of molecular flexibility is not negligible. Our results are in good agreement with experimental data, as well as with virials given by recent empirical equations of state, although some discrepancies are observed for H{sub 2} between 100 and 200 K.
Quantum Brownian Motions and Navier-Stokes Weakly Turbulence — a Path Integral Study
NASA Astrophysics Data System (ADS)
Botelho, Luiz C. L.
In this paper, we present a new method to solve exactly the Schrödinger Harmonic oscillator wave equation in the presence of time-dependent parameter. We also apply such technique to solve exactly the problem of random frequency averaged quantum propagator of a harmonic oscillator with white-noise statistics frequency. We still apply our technique to solve exactly the Brownian Quantum Oscillator in the presence of an electric field. Finally, we use these quantum mechanic techniques to solve exactly the Statistical-Turbulence of the Navier-Stokes in a region of fluid random stirring weakly (analytical) coupling through time-dependent Euclidean-Quantum oscillators path-integrals.
Ab initio Path Integral Molecular Dynamics Based on Fragment Molecular Orbital Method
NASA Astrophysics Data System (ADS)
Fujita, Takatoshi; Watanabe, Hirofumi; Tanaka, Shigenori
2009-10-01
We have developed an ab initio path integral molecular dynamics method based on the fragment molecular orbital method. This “FMO-PIMD” method can treat both nuclei and electrons quantum mechanically, and is useful to simulate large hydrogen-bonded systems with high accuracy. After a benchmark calculation for water monomer, water trimer and glycine pentamer have been studied using the FMO-PIMD method to investigate nuclear quantum effects on structure and molecular interactions. The applicability of the present approach is demonstrated through a number of test calculations.
Formation of bound states in expanded metal studied via path integral molecular dynamics
NASA Astrophysics Data System (ADS)
Deymier, P. A.; Oh, Ki-Dong
2004-03-01
The usefulness of the restricted path integral molecular dynamics method for the study of strongly correlated electrons is demonstrated by studying the formation of bound electronic states in a half-filled expanded three-dimensional hydrogenoid body-centred cubic lattice at finite temperature. Starting from a metallic state with one-component plasma character, we find that bound electrons form upon expansion of the lattice. The bound electrons are spatially localized with their centre for the motion of gyration located at ionic positions. The number of bound electrons increases monotonically with decreasing density.
NASA Astrophysics Data System (ADS)
Krajewski, Florian R.; Müser, Martin H.
2005-07-01
The spectral density of quantum mechanical Frenkel Kontorova chains moving in disordered, external potentials is investigated by means of path-integral molecular dynamics. If the second moment of the embedding potential is well defined (roughness exponent H=0), there is one regime in which the chain is pinned (large masses m of chain particles) and one in which it is unpinned (small m). If the embedding potential can be classified as a random walk on large length scales ( H=1/2), then the chain is always pinned irrespective of the value of m. For H=1/2, two phonon-like branches appear in the spectra.
Path-integral molecular dynamics simulations for water anion clusters (HO)5- and (DO)5-
NASA Astrophysics Data System (ADS)
Takayanagi, Toshiyuki; Yoshikawa, Takehiro; Motegi, Haruki; Shiga, Motoyuki
2009-11-01
Quantum path-integral molecular dynamics simulations have been performed for the (HO)5- and (DO)5- anion clusters on the basis of a semiempirical one-electron pseudopotential-polarization model. Due to larger zero-point vibrational amplitudes for H atoms than that of D atoms, hydrogen-bond lengths in the (HO)5- cluster are slightly larger than those in (DO)5-. The distribution of the vertical detachment energies for (HO)5- also show a broader feature than that for (DO)5-. The present PIMD simulations thus demonstrate the importance of nuclear quantum effects in water anion clusters.
NASA Astrophysics Data System (ADS)
Kapila, Vivek; Deymier, Pierre; Runge, Keith
2011-10-01
Several areas of study including heavy ion beam, large scale laser, and high pressure or Thomson scattering studies necessitate a fundamental understanding of warm dense matter (WDM) i.e. matter at high temperature and high density. The WDM regime, however, lacks any adequate highly developed class of simulation methods. Recent progress to address this deficit has been the development of orbital-free Density Functional Theory (ofDFT). However, scant benchmark information is available on temperature and pressure dependence of simple but realistic models in WDM regime. The present work aims to fill this critical gap using the restricted path-integral molecular dynamics (rPIMD) method. Within the discrete path integral representation, electrons are described as harmonic necklaces. Quantum exchange takes the form of cross linking between electron necklaces. The fermion sign problem is addressed by restricting the density matrix to positive values. The molecular dynamics algorithm is employed to sample phase space. Here, we focus on the behavior of strongly correlated electron plasmas under WDM conditions. We compute the kinetic and potential energies and compare them to those obtained with the ofDFT method. Several areas of study including heavy ion beam, large scale laser, and high pressure or Thomson scattering studies necessitate a fundamental understanding of warm dense matter (WDM) i.e. matter at high temperature and high density. The WDM regime, however, lacks any adequate highly developed class of simulation methods. Recent progress to address this deficit has been the development of orbital-free Density Functional Theory (ofDFT). However, scant benchmark information is available on temperature and pressure dependence of simple but realistic models in WDM regime. The present work aims to fill this critical gap using the restricted path-integral molecular dynamics (rPIMD) method. Within the discrete path integral representation, electrons are described as
Path Integral Molecular Dynamics for Hydrogen with Orbital-Free Density Functional Theory
NASA Astrophysics Data System (ADS)
Runge, Keith; Karasiev, Valentin; Deymier, Pierre
2014-03-01
The computational bottleneck for performing path-integral molecular dynamics (PIMD) for nuclei on a first principles electronic potential energy surface has been the speed with which forces from the electrons can be generated. Recent advances in orbital-free density functional theory (OF-DFT) not only allow for faster generation of first principles forces but also include the effects of temperature on the electron density. We will present results of calculations on hydrogen in warm dense matter conditions where the protons are described by PIMD and the electrons by OF-DFT. Work supported by U.S. Dept. of Energy, grant DE-SC0002139.
Development of a Pulsed 2-Micron Integrated Path Differential Absorption Lidar for CO2 Measurement
NASA Technical Reports Server (NTRS)
Singh, Upendra N.; Yu, Jirong; Petros, Mulugeta; Refaat, Tamer; Refaat, Tamer
2013-01-01
Atmospheric carbon dioxide (CO2) is an important greenhouse gas that significantly contributes to the carbon cycle and global radiation budget on Earth. Active remote sensing of CO2 is important to address several limitations that contend with passive sensors. A 2-micron double-pulsed, Integrated Path Differential Absorption (IPDA) lidar instrument for ground and airborne atmospheric CO2 concentration measurements via direct detection method is being developed at NASA Langley Research Center. This active remote sensing instrument will provide an alternate approach of measuring atmospheric CO2 concentrations with significant advantages. A high energy pulsed approach provides high-precision measurement capability by having high signal-to-noise ratio level and unambiguously eliminates the contamination from aerosols and clouds that can bias the IPDA measurement. Commercial, on the shelf, components are implemented for the detection system. Instrument integration will be presented in this paper as well as a background for CO2 measurement at NASA Langley research Center
High-order sampling schemes for path integrals and Gaussian chain simulations of polymers
Müser, Martin H.; Müller, Marcus
2015-05-07
In this work, we demonstrate that path-integral schemes, derived in the context of many-body quantum systems, benefit the simulation of Gaussian chains representing polymers. Specifically, we show how to decrease discretization corrections with little extra computation from the usual O(1/P{sup 2}) to O(1/P{sup 4}), where P is the number of beads representing the chains. As a consequence, high-order integrators necessitate much smaller P than those commonly used. Particular emphasis is placed on the questions of how to maintain this rate of convergence for open polymers and for polymers confined by a hard wall as well as how to ensure efficient sampling. The advantages of the high-order sampling schemes are illustrated by studying the surface tension of a polymer melt and the interface tension in a binary homopolymers blend.
Development of a pulsed 2-micron integrated path differential absorption lidar for CO2 measurement
NASA Astrophysics Data System (ADS)
Singh, Upendra N.; Yu, Jirong; Petros, Mulugeta; Refaat, Tamer; Reithmaier, Karl
2013-09-01
Atmospheric carbon dioxide (CO2) is an important greenhouse gas that significantly contributes to the carbon cycle and global radiation budget on Earth. Active remote sensing of CO2 is important to address several limitations that contend with passive sensors. A 2-micron double-pulsed, Integrated Path Differential Absorption (IPDA) lidar instrument for ground and airborne atmospheric CO2 concentration measurements via direct detection method is being developed at NASA Langley Research Center. This active remote sensing instrument will provide an alternate approach of measuring atmospheric CO2 concentrations with significant advantages. A high energy pulsed approach provides high-precision measurement capability by having high signal-to-noise ratio level and unambiguously eliminates the contamination from aerosols and clouds that can bias the IPDA measurement. Commercial, on the shelf, components are implemented for the detection system. Instrument integration will be presented in this paper as well as a background for CO2 measurement at NASA Langley research Center.
A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals
Sinitskiy, Anton V.; Voth, Gregory A.
2015-09-07
Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman’s imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.
Schütt, Ole; Sebastiani, Daniel
2013-04-05
We investigate the quantum-mechanical delocalization of hydrogen in rotational symmetric molecular systems. To this purpose, we perform ab initio path integral molecular dynamics simulations of a methanol molecule to characterize the quantum properties of hydrogen atoms in a representative system by means of their real-space and momentum-space densities. In particular, we compute the spherically averaged momentum distribution n(k) and the pseudoangular momentum distribution n(kθ). We interpret our results by comparing them to path integral samplings of a bare proton in an ideal torus potential. We find that the hydroxyl hydrogen exhibits a toroidal delocalization, which leads to characteristic fingerprints in the line shapes of the momentum distributions. We can describe these specific spectroscopic patterns quantitatively and compute their onset as a function of temperature and potential energy landscape. The delocalization patterns in the projected momentum distribution provide a promising computational tool to address the intriguing phenomenon of quantum delocalization in condensed matter and its spectroscopic characterization. As the momentum distribution n(k) is also accessible through Nuclear Compton Scattering experiments, our results will help to interpret and understand future measurements more thoroughly.
Contact Potential Instability in the Path-Integral Description of Itinerant Ferromagnetism
NASA Astrophysics Data System (ADS)
Vermeyen, E.; Tempere, J.
2015-05-01
It has long been predicted that a two-component non-localized Fermi gas will exhibit spontaneous polarization for sufficiently strong repulsive interactions, a phenomenon which is called itinerant ferromagnetism. Recent experiments with ultracold atomic gases have reached the interaction strength for which theoretical models have predicted the occurrence of the normal-to-itinerant-ferromagnetic phase transition, but so far this transition has not been observed. The instability of the repulsive branch of the Feshbach resonance prevents the formation of the itinerant ferromagnetic state, but it is not clear whether this is the only instability impeding its experimental realization. In this article, we use the path-integral formalism with density fields in the Hubbard-Stratonovich transformation to study the stability of a homogeneous two-component Fermi gas with contact interactions. Within the saddle-point approximation we show that none of the extrema of the action are minima, meaning all extrema are unstable to small density fluctuations. This implies a more general mechanical instability of the polarized (itinerant ferromagnetic) and normal states of the system in the path-integral formalism. We find that it is important to consider the stability of the system when studying itinerant ferromagnetism. Since (mechanical) stability may be influenced by the details of the interaction potential, we suggest the use of a more realistic potential than the contact potential in future theoretical descriptions.
Accelerating Ab Initio Path Integral Simulations via Imaginary Multiple-Timestepping.
Cheng, Xiaolu; Herr, Jonathan D; Steele, Ryan P
2016-04-12
This work investigates the use of multiple-timestep schemes in imaginary time for computationally efficient ab initio equilibrium path integral simulations of quantum molecular motion. In the simplest formulation, only every n(th) path integral replica is computed at the target level of electronic structure theory, whereas the remaining low-level replicas still account for nuclear motion quantum effects with a more computationally economical theory. Motivated by recent developments for multiple-timestep techniques in real-time classical molecular dynamics, both 1-electron (atomic-orbital basis set) and 2-electron (electron correlation) truncations are shown to be effective. Structural distributions and thermodynamic averages are tested for representative analytic potentials and ab initio molecular examples. Target quantum chemistry methods include density functional theory and second-order Møller-Plesset perturbation theory, although any level of theory is formally amenable to this framework. For a standard two-level splitting, computational speedups of 1.6-4.0x are observed when using a 4-fold reduction in time slices; an 8-fold reduction is feasible in some cases. Multitiered options further reduce computational requirements and suggest that quantum mechanical motion could potentially be obtained at a cost not significantly different from the cost of classical simulations.
van Zon, Ramses; Hernández de la Peña, Lisandro; Peslherbe, Gilles H; Schofield, Jeremy
2008-10-01
In this paper, the imaginary-time path-integral representation of the canonical partition function of a quantum system and nonequilibrium work fluctuation relations are combined to yield methods for computing free-energy differences in quantum systems using nonequilibrium processes. The path-integral representation is isomorphic to the configurational partition function of a classical field theory, to which a natural but fictitious Hamiltonian dynamics is associated. It is shown that if this system is prepared in an equilibrium state, after which a control parameter in the fictitious Hamiltonian is changed in a finite time, then formally the Jarzynski nonequilibrium work relation and the Crooks fluctuation relation hold, where work is defined as the change in the energy as given by the fictitious Hamiltonian. Since the energy diverges for the classical field theory in canonical equilibrium, two regularization methods are introduced which limit the number of degrees of freedom to be finite. The numerical applicability of the methods is demonstrated for a quartic double-well potential with varying asymmetry. A general parameter-free smoothing procedure for the work distribution functions is useful in this context.
Path integral representation of Lorentzian spinfoam model, asymptotics and simplicial geometries
NASA Astrophysics Data System (ADS)
Han, Muxin; Krajewski, Thomas
2014-01-01
A new path integral representation of Lorentzian Engle-Pereira-Rovelli-Livine spinfoam model is derived by employing the theory of unitary representation of {SL}(2, {C}). The path integral representation is taken as a starting point of semiclassical analysis. The relation between the spinfoam model and classical simplicial geometry is studied via the large-spin asymptotic expansion of the spinfoam amplitude with all spins uniformly large. More precisely, in the large-spin regime, there is an equivalence between the spinfoam critical configuration (with certain nondegeneracy assumption) and a classical Lorentzian simplicial geometry. Such an equivalence relation allows us to classify the spinfoam critical configurations by their geometrical interpretations, via two types of solution-generating maps. The equivalence between spinfoam critical configuration and simplical geometry also allows us to define the notion of globally oriented and time-oriented spinfoam critical configuration. It is shown that only at the globally oriented and time-oriented spinfoam critical configuration, the leading-order contribution of spinfoam large-spin asymptotics gives precisely an exponential of Lorentzian Regge action of General Relativity. At all other (unphysical) critical configurations, spinfoam large-spin asymptotics modifies the Regge action at the leading-order approximation.
A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals.
Sinitskiy, Anton V; Voth, Gregory A
2015-09-07
Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman's imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.
Interactions of the polarization and the sun compass in path integration of desert ants.
Lebhardt, Fleur; Ronacher, Bernhard
2014-08-01
Desert ants, Cataglyphis fortis, perform large-scale foraging trips in their featureless habitat using path integration as their main navigation tool. To determine their walking direction they use primarily celestial cues, the sky's polarization pattern and the sun position. To examine the relative importance of these two celestial cues, we performed cue conflict experiments. We manipulated the polarization pattern experienced by the ants during their outbound foraging excursions, reducing it to a single electric field (e-)vector direction with a linear polarization filter. The simultaneous view of the sun created situations in which the directional information of the sun and the polarization compass disagreed. The heading directions of the homebound runs recorded on a test field with full view of the natural sky demonstrate that none of both compasses completely dominated over the other. Rather the ants seemed to compute an intermediate homing direction to which both compass systems contributed roughly equally. Direct sunlight and polarized light are detected in different regions of the ant's compound eye, suggesting two separate pathways for obtaining directional information. In the experimental paradigm applied here, these two pathways seem to feed into the path integrator with similar weights.
NASA Astrophysics Data System (ADS)
Barth, A. M.; Vagov, A.; Axt, V. M.
2016-09-01
We present a numerical path-integral iteration scheme for the low-dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modeled pure-dephasing-type coupling to a continuum of harmonic oscillators representing, e.g., phonons, and further environmental interactions inducing non-Hamiltonian dynamics in the inner system represented, e.g., by Lindblad-type dissipation or relaxation. Our formulation of the path-integral method allows for a numerically exact treatment of the coupling to the oscillator modes and moreover is general enough to provide a natural way to include Markovian processes that are sufficiently described by rate equations. We apply this new formalism to a model of a single semiconductor quantum dot which includes the coupling to longitudinal acoustic phonons for two cases: (a) external laser excitation taking into account a phenomenological radiative decay of the excited dot state and (b) a coupling of the quantum dot to a single mode of an optical cavity taking into account cavity photon losses.
Path integral method for predicting relative binding affinities of protein-ligand complexes
Mulakala, Chandrika; Kaznessis, Yiannis N.
2009-01-01
We present a novel approach for computing biomolecular interaction binding affinities based on a simple path integral solution of the Fokker-Planck equation. Computing the free energy of protein-ligand interactions can expedite structure-based drug design. Traditionally, the problem is seen through the lens of statistical thermodynamics. The computations can become, however, prohibitively long for the change in the free energy upon binding to be determined accurately. In this work we present a different approach based on a stochastic kinetic formalism. Inspired by Feynman's path integral formulation, we extend the theory to classical interacting systems. The ligand is modeled as a Brownian particle subjected to the effective non-bonding interaction potential of the receptor. This allows the calculation of the relative binding affinities of interacting biomolecules in water to be computed as a function of the ligand's diffusivity and the curvature of the potential surface in the vicinity of the binding minimum. The calculation is thus exceedingly rapid. In test cases, the correlation coefficient between actual and computed free energies is >0.93 for accurate data-sets. PMID:19275144
Transport properties of liquid para-hydrogen: The path integral centroid molecular dynamics approach
NASA Astrophysics Data System (ADS)
Yonetani, Yoshiteru; Kinugawa, Kenichi
2003-11-01
Several fundamental transport properties of a quantum liquid para-hydrogen (p-H2) at 17 K have been numerically evaluated by means of the quantum dynamics simulation called the path integral centroid molecular dynamics (CMD). For comparison, classical molecular dynamics (MD) simulations have also been performed under the same condition. In accordance with the previous path integral simulations, the calculated static properties of the liquid agree well with the experimental results. For the diffusion coefficient, thermal conductivity, and shear viscosity, the CMD predicts the values closer to the experimental ones though the classical MD results are far from the reality. The agreement of the CMD result with the experimental one is especially good for the shear viscosity with the difference less than 5%. The calculated diffusion coefficient and the thermal conductivity agree with the experimental values at least in the same order. We predict that the ratio of bulk viscosity to shear viscosity for liquid p-H2 is much larger than classical van der Waals simple liquids such as rare gas liquids.
Tanizaki, Yuya; Koike, Takayuki
2014-12-15
Picard–Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly. After discussing basic properties of real-time path integrals on Lefschetz thimbles, we demonstrate its computational method in a concrete way by solving three simple examples of quantum mechanics. It is applied to quantum mechanics of a double-well potential, and quantum tunneling is discussed. We identify all of the complex saddle points of the classical action, and their properties are discussed in detail. However a big theoretical difficulty turns out to appear in rewriting the original path integral into a sum of path integrals on Lefschetz thimbles. We discuss generality of that problem and mention its importance. Real-time tunneling processes are shown to be described by those complex saddle points, and thus semi-classical description of real-time quantum tunneling becomes possible on solid ground if we could solve that problem. - Highlights: • Real-time path integral is studied based on Picard–Lefschetz theory. • Lucid demonstration is given through simple examples of quantum mechanics. • This technique is applied to quantum mechanics of the double-well potential. • Difficulty for practical applications is revealed, and we discuss its generality. • Quantum tunneling is shown to be closely related to complex classical solutions.
Wolbers, Thomas; Wiener, Jan M; Mallot, Hanspeter A; Büchel, Christian
2007-08-29
Path integration, the ability to sense self-motion for keeping track of changes in orientation and position, constitutes a fundamental mechanism of spatial navigation and a keystone for the development of cognitive maps. Whereas animal path integration is predominantly supported by the head-direction, grid, and place cell systems, the neural foundations are not well understood in humans. Here we used functional magnetic resonance imaging and a virtual rendition of a triangle completion paradigm to test whether human path integration recruits a cortical system similar to that of rodents and nonhuman primates. Participants traveled along two legs of a triangle before pointing toward the starting location. In accordance with animal models, stronger right hippocampal activation predicted more accurate updating of the starting location on a trial-by-trial basis. Moreover, between-subjects fluctuations in response consistency were negatively correlated with bilateral hippocampal and medial prefrontal activation, and bilateral recruitment of the human motion complex (hMT+) covaried with individual path integration capability. Given that these effects were absent in a perceptual control task, the present study provides the first evidence that visual path integration is related to the dynamic interplay of self-motion processing in hMT+, higher-level spatial processes in the hippocampus, and spatial working memory in medial prefrontal cortex.
Zheng, Zewei; Zou, Yao
2016-11-01
This paper investigates the path following control problem for an unmanned airship in the presence of unknown wind and uncertainties. The backstepping technique augmented by a robust adaptive radial basis function neural network (RBFNN) is employed as the main control framework. Based on the horizontal dynamic model of the airship, an improved adaptive integral line-of-sight (LOS) guidance law is first proposed, which suits any parametric paths. The guidance law calculates the desired yaw angle and estimates the wind. Then the controller is extended to cope with the airship yaw tracking and velocity control by resorting to the augmented backstepping technique. The uncertainties of the dynamics are compensated by using the robust RBFNNs. Each robust RBFNN utilizes an nth-order smooth switching function to combine a conventional RBFNN with a robust control. The conventional RBFNN dominates in the neural active region, while the robust control retrieves the transient outside the active region, so that the stability range can be widened. Stability analysis shows that the controlled closed-loop system is globally uniformly ultimately bounded. Simulations are provided to validate the effectiveness of the proposed control approach.
NASA Astrophysics Data System (ADS)
Voronov, Aleksandr V.; Tret'yakov, Evgeniy V.; Shuvalov, Vladimir V.
2004-06-01
Based on the path-integration technique and the Metropolis method, the original calculation scheme is developed for solving the problem of light propagation through highly scattering objects. The elimination of calculations of 'unnecessary' realisations and the phenomenological description of processes of multiple small-angle scattering provided a drastic increase (by nine and more orders of magnitude) in the calculation rate, retaining the specific features of the problem (consideration of spatial inhomogeneities, boundary conditions, etc.). The scheme allows one to verify other fast calculation algorithms and to obtain information required to reconstruct the internal structure of highly scattering objects (of size ~1000 scattered lengths and more) by the method of diffusion optical tomography.
A Path Integral Approach to Option Pricing with Stochastic Volatility: Some Exact Results
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.
1997-12-01
The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic. The derivation of the price of a security derivative with stochastic volatility is reviewed starting from the first principles of finance. The equation of Merton and Garman is then recast using the path integration technique of theoretical physics. The price of the stock option is shown to be the analogue of the Schrödinger wavefunction of quantum mechanics and the exact Hamiltonian and Lagrangian of the system is obtained. The results of Hull and White are generalized to the case when stock price and volatility have non-zero correlation. Some exact results for pricing stock options for the general correlated case are derived.
WORM ALGORITHM PATH INTEGRAL MONTE CARLO APPLIED TO THE 3He-4He II SANDWICH SYSTEM
NASA Astrophysics Data System (ADS)
Al-Oqali, Amer; Sakhel, Asaad R.; Ghassib, Humam B.; Sakhel, Roger R.
2012-12-01
We present a numerical investigation of the thermal and structural properties of the 3He-4He sandwich system adsorbed on a graphite substrate using the worm algorithm path integral Monte Carlo (WAPIMC) method [M. Boninsegni, N. Prokof'ev and B. Svistunov, Phys. Rev. E74, 036701 (2006)]. For this purpose, we have modified a previously written WAPIMC code originally adapted for 4He on graphite, by including the second 3He-component. To describe the fermions, a temperature-dependent statistical potential has been used. This has proven very effective. The WAPIMC calculations have been conducted in the millikelvin temperature regime. However, because of the heavy computations involved, only 30, 40 and 50 mK have been considered for the time being. The pair correlations, Matsubara Green's function, structure factor, and density profiles have been explored at these temperatures.
NASA Astrophysics Data System (ADS)
Lee, Mi Kyung; Huo, Pengfei; Coker, David F.
2016-05-01
This article reviews recent progress in the theoretical modeling of excitation energy transfer (EET) processes in natural light harvesting complexes. The iterative partial linearized density matrix path-integral propagation approach, which involves both forward and backward propagation of electronic degrees of freedom together with a linearized, short-time approximation for the nuclear degrees of freedom, provides an accurate and efficient way to model the nonadiabatic quantum dynamics at the heart of these EET processes. Combined with a recently developed chromophore-protein interaction model that incorporates both accurate ab initio descriptions of intracomplex vibrations and chromophore-protein interactions treated with atomistic detail, these simulation tools are beginning to unravel the detailed EET pathways and relaxation dynamics in light harvesting complexes.
Path-integral action of a particle in the noncommutative plane.
Gangopadhyay, Sunandan; Scholtz, Frederik G
2009-06-19
Noncommutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on noncommutative configuration space. Taking this as a departure point, we formulate a coherent state approach to the path-integral representation of the transition amplitude. From this we derive an action for a particle moving in the noncommutative plane and in the presence of an arbitrary potential. We find that this action is nonlocal in time. However, this nonlocality can be removed by introducing an auxilary field, which leads to a second class constrained system that yields the noncommutative Heisenberg algebra upon quantization. Using this action, the propagator of the free particle and harmonic oscillator are computed explicitly.
Quantum Mechanical Single Molecule Partition Function from PathIntegral Monte Carlo Simulations
Chempath, Shaji; Bell, Alexis T.; Predescu, Cristian
2006-10-01
An algorithm for calculating the partition function of a molecule with the path integral Monte Carlo method is presented. Staged thermodynamic perturbation with respect to a reference harmonic potential is utilized to evaluate the ratio of partition functions. Parallel tempering and a new Monte Carlo estimator for the ratio of partition functions are implemented here to achieve well converged simulations that give an accuracy of 0.04 kcal/mol in the reported free energies. The method is applied to various test systems, including a catalytic system composed of 18 atoms. Absolute free energies calculated by this method lead to corrections as large as 2.6 kcal/mol at 300 K for some of the examples presented.
Excitonic effects in two-dimensional semiconductors: Path integral Monte Carlo approach
Velizhanin, Kirill A.; Saxena, Avadh
2015-11-01
The most striking features of novel two-dimensional semiconductors (e.g., transition metal dichalcogenide monolayers or phosphorene) is a strong Coulomb interaction between charge carriers resulting in large excitonic effects. In particular, this leads to the formation of multicarrier bound states upon photoexcitation (e.g., excitons, trions, and biexcitons), which could remain stable at near-room temperatures and contribute significantly to the optical properties of such materials. In our work we have used the path integral Monte Carlo methodology to numerically study properties of multicarrier bound states in two-dimensional semiconductors. Specifically, we have accurately investigated and tabulated the dependence of single-exciton, trion, and biexciton binding energies on the strength of dielectric screening, including the limiting cases of very strong and very weak screening. Our results of this work are potentially useful in the analysis of experimental data and benchmarking of theoretical and computational models.
Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics
NASA Astrophysics Data System (ADS)
Everett, Allen
2004-06-01
We consider two approaches to evading paradoxes in quantum mechanics with closed timelike curves. In a model similar to Politzer’s, assuming pure states and using path integrals, we show that the problems of paradoxes and of unitarity violation are related; preserving unitarity avoids paradoxes by modifying the time evolution so that improbable events become certain. Deutsch has argued, using the density matrix, that paradoxes do not occur in the “many worlds interpretation.” We find that in this approach account must be taken of the resolution time of the device that detects objects emerging from a wormhole or other time machine. When this is done one finds that this approach is viable only if macroscopic objects traversing a wormhole interact with it so strongly that they are broken into microscopic fragments.
Excitonic effects in two-dimensional semiconductors: Path integral Monte Carlo approach
Velizhanin, Kirill A.; Saxena, Avadh
2015-11-01
The most striking features of novel two-dimensional semiconductors (e.g., transition metal dichalcogenide monolayers or phosphorene) is a strong Coulomb interaction between charge carriers resulting in large excitonic effects. In particular, this leads to the formation of multicarrier bound states upon photoexcitation (e.g., excitons, trions, and biexcitons), which could remain stable at near-room temperatures and contribute significantly to the optical properties of such materials. In our work we have used the path integral Monte Carlo methodology to numerically study properties of multicarrier bound states in two-dimensional semiconductors. Specifically, we have accurately investigated and tabulated the dependence of single-exciton, trion, and biexcitonmore » binding energies on the strength of dielectric screening, including the limiting cases of very strong and very weak screening. Our results of this work are potentially useful in the analysis of experimental data and benchmarking of theoretical and computational models.« less
Torsional path integral Monte Carlo method for the quantum simulation of large molecules
NASA Astrophysics Data System (ADS)
Miller, Thomas F.; Clary, David C.
2002-05-01
A molecular application is introduced for calculating quantum statistical mechanical expectation values of large molecules at nonzero temperatures. The Torsional Path Integral Monte Carlo (TPIMC) technique applies an uncoupled winding number formalism to the torsional degrees of freedom in molecular systems. The internal energy of the molecules ethane, n-butane, n-octane, and enkephalin are calculated at standard temperature using the TPIMC technique and compared to the expectation values obtained using the harmonic oscillator approximation and a variational technique. All studied molecules exhibited significant quantum mechanical contributions to their internal energy expectation values according to the TPIMC technique. The harmonic oscillator approximation approach to calculating the internal energy performs well for the molecules presented in this study but is limited by its neglect of both anharmonicity effects and the potential coupling of intramolecular torsions.
Path integral study of the correlated electronic states of Na4-Na6
NASA Astrophysics Data System (ADS)
Hall, Randall W.
1990-12-01
Feynman's path integral formulation of quantum mechanics is used to study the correlated electronic states of Na4-Na6. Two types of simulations are performed: in the first, the nuclei are allowed to move at finite temperature in order to find the most stable geometries. In agreement with previous calculations, we find that planar structures are the most stable and that there is significant vibrational amplitude at finite temperatures, indicating that the Born-Oppenheimer surface is relatively flat. In the second type of simulation, the nuclei are held fixed at symmetric and asymmetric geometries and the correlated electron density is found. Our results show that the electrons are localized, rather than delocalized as previous workers have concluded from examination of the single-particle orbitals. We find that the best picture of these clusters is that they contain three-center, two-electron bonds.
Gaussian white noise analysis and its application to Feynman path integral
NASA Astrophysics Data System (ADS)
Suryawan, Herry Pribawanto
2016-02-01
In applied science, Gaussian white noise (the time derivative of Brownian motion) is often chosen as a mathematical idealization of phenomena involving sudden and extremely large fluctuations. It is also possible to define and study Gaussian white noise in a mathematically rigorous framework. In this survey paper we review the Gaussian white noise as an object in an infinite dimensional topological vector space. A brief construction of Gaussian white noise space and Gaussian white noise distributions will be presented. Gaussian white noise analysis provides a framework which offers various generalization of concept known from finite dimensional analysis to the infinite dimensional case, among them are differential operators, Fourier transform, and distribution theory. We will also present some recent developments and results on the application of Gaussian white noise theory to Feynman's path integral approach for quantum mechanics.
NASA Astrophysics Data System (ADS)
Yoshikawa, Takehiro; Sugawara, Shuichi; Takayanagi, Toshiyuki; Shiga, Motoyuki; Tachikawa, Masanori
2012-02-01
Path-integral molecular dynamics simulations have been performed for porphycene and its isotopic variants in order to understand the effect of isotopic substitution of inner protons on the double proton transfer mechanism. We have used an on-the-fly direct dynamics technique at the semiempirical PM6 level combined with specific reaction parameterization. Our quantum simulations show that double proton transfer of the unsubstituted porphycene at T = 300 K mainly occurs via a so-called concerted mechanism through the D2h second-order saddle point. In addition, we found that both isotopic substitution and temperature significantly affect the double proton transfer mechanism. For example, the contribution of the stepwise mechanism increases with a temperature increase. We have also carried out hypothetical simulations with the porphycene configurations being completely planar. It has been found that out-of-plane vibrational motions significantly decrease the contribution of the concerted proton transfer mechanism.
NASA Astrophysics Data System (ADS)
Witt, Alexander; Ivanov, Sergei D.; Shiga, Motoyuki; Forbert, Harald; Marx, Dominik
2009-05-01
Centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD) are two conceptually distinct extensions of path integral molecular dynamics that are able to generate approximate quantum dynamics of complex molecular systems. Both methods can be used to compute quasiclassical time correlation functions which have direct application in molecular spectroscopy; in particular, to infrared spectroscopy via dipole autocorrelation functions. The performance of both methods for computing vibrational spectra of several simple but representative molecular model systems is investigated systematically as a function of temperature and isotopic substitution. In this context both CMD and RPMD feature intrinsic problems which are quantified and investigated in detail. Based on the obtained results guidelines for using CMD and RPMD to compute infrared spectra of molecular systems are provided.
Path integral centroid molecular dynamics simulation of para-hydrogen sandwiched by graphene sheets
NASA Astrophysics Data System (ADS)
Minamino, Yuki; Kinugawa, Kenichi
2016-11-01
The carbon-hydrogen composite systems of para-hydrogen (p-H2) sandwiched by a couple of graphene sheets have been investigated by means of path integral centroid molecular dynamics simulations at 17 K. It has been shown that sandwiched hydrogen is liquid-like but p-H2 molecules are preferably adsorbed onto the graphene sheets because of attractive graphene-hydrogen interaction. The diffusion coefficient of p-H2 molecules in the direction parallel to the graphene sheets is comparable to that in pure liquid p-H2. There exists a characteristic mode of 140 cm-1 of the p-H2 molecules, attributed to adsorption-binding motion perpendicular to the graphene sheets.
NASA Astrophysics Data System (ADS)
Wang, Qi; Suzuki, Kimichi; Nagashima, Umpei; Tachikawa, Masanori; Yan, Shiwei
2013-11-01
The geometric isotope effects on the structures of hydrated chloride ionic hydrogen bonded clusters are explored by carrying out path integral molecular dynamics simulations. First, an outer shell coordinate is selected to display the rearrangement of single and multi hydration shell cluster structures. Next, to show the competition of intramolecular and intermolecular nuclear quantum effects, the intramolecular OH∗ stretching and intermolecular ion-water wagging motions are studied for single and multi shell structures, respectively. The results indicate that the intermolecular nuclear quantum effects stabilize the ionic hydrogen bonds in single shell structures, while they are destabilized through the competition with intramolecular nuclear quantum effects in multi shell structures. In addition, the correlations between ion-water stretching motion and other cluster vibrational coordinates are discussed. The results indicate that the intermolecular nuclear quantum effects on the cluster structures are strongly related to the cooperation of the water-water hydrogen bond interactions.
NASA Astrophysics Data System (ADS)
Reilly, Anthony M.; Habershon, Scott; Morrison, Carole A.; Rankin, David W. H.
2010-03-01
Path-integral molecular dynamics (PIMD) simulations with an empirical interaction potential have been used to determine the experimental equilibrium structure of solid nitromethane at 4.2 and 15 K. By comparing the time-averaged molecular structure determined in a PIMD simulation to the calculated minimum-energy (zero-temperature) molecular structure, we have derived structural corrections that describe the effects of thermal motion. These corrections were subsequently used to determine the equilibrium structure of nitromethane from the experimental time-averaged structure. We find that the corrections to the intramolecular and intermolecular bond distances, as well as to the torsion angles, are quite significant, particularly for those atoms participating in the anharmonic motion of the methyl group. Our results demonstrate that simple harmonic models of thermal motion may not be sufficiently accurate, even at low temperatures, while molecular simulations employing more realistic potential-energy surfaces can provide important insight into the role and magnitude of anharmonic atomic motions.
NASA Astrophysics Data System (ADS)
Ananth, Nandini
2013-09-01
We introduce mapping-variable ring polymer molecular dynamics (MV-RPMD), a model dynamics for the direct simulation of multi-electron processes. An extension of the RPMD idea, this method is based on an exact, imaginary time path-integral representation of the quantum Boltzmann operator using continuous Cartesian variables for both electronic states and nuclear degrees of freedom. We demonstrate the accuracy of the MV-RPMD approach in calculations of real-time, thermal correlation functions for a range of two-state single-mode model systems with different coupling strengths and asymmetries. Further, we show that the ensemble of classical trajectories employed in these simulations preserves the Boltzmann distribution and provides a direct probe into real-time coupling between electronic state transitions and nuclear dynamics.
Low-temperature metallic liquid hydrogen: an ab-initio path-integral molecular dynamics perspective
NASA Astrophysics Data System (ADS)
Chen, Ji; Li, Xin-Zheng; Zhang, Qianfan; Probert, Matthew; Pickard, Chris; Needs, Richard; Michaelides, Angelos; Wang, Enge
2013-03-01
Experiments and computer simulations have shown that the melting temperature of solid hydrogen drops with pressure above about 65 GPa, suggesting that a low temperature liquid state might exist. It has also been suggested that this liquid state might be non-molecular and metallic, although evidence for such behaviour is lacking. Using a combination of ab initio path-integral molecular dynamics and the two-phase methods, we have simulated the melting of solid hydrogen under finite temperatures. We found an atomic solid phase from 500 to 800 GPa which melts at < 200 K. Beyond this and up to pressures of 1,200 GPa a metallic atomic liquid is stable at temperatures as low as 50 K. The quantum motion of the protons is critical to the low melting temperature in this system as ab initio simulations with classical nuclei lead to a considerably higher melting temperature of ~300 K across the entire pressure range considered.
Hydrogen and muonium in diamond: A path-integral molecular dynamics simulation
NASA Astrophysics Data System (ADS)
Herrero, Carlos P.; Ramírez, Rafael; Hernández, Eduardo R.
2006-06-01
Isolated hydrogen, deuterium, and muonium in diamond have been studied by path-integral molecular dynamics simulations in the canonical ensemble. Finite-temperature properties of these point defects were analyzed in the range from 100 to 800K . Interatomic interactions were modeled by a tight-binding potential fitted to density-functional calculations. The most stable position for these hydrogenic impurities is found at the C-C bond center. Vibrational frequencies have been obtained from a linear-response approach, based on correlations of atom displacements at finite temperatures. The results show a large anharmonic effect in impurity vibrations at the bond center site, which hardens the vibrational modes with respect to a harmonic approximation. Zero-point motion causes an appreciable shift of the defect level in the electronic gap, as a consequence of electron-phonon interaction. This defect level goes down by 70meV when replacing hydrogen by muonium.
Low-temperature anharmonicity of barium titanate: A path-integral molecular-dynamics study
NASA Astrophysics Data System (ADS)
Geneste, Grégory; Dammak, Hichem; Hayoun, Marc; Thiercelin, Mickael
2013-01-01
We investigate the influence of quantum effects on the dielectric and piezoelectric properties of barium titanate in its (low-temperature) rhombohedral phase, and show the strongly anharmonic character of this system even at low temperature. For this purpose, we perform path-integral molecular-dynamics simulations under fixed pressure and fixed temperature, using an efficient Langevin thermostat-barostat, and an effective Hamiltonian derived from first-principles calculations. The quantum fluctuations are shown to significantly enhance the static dielectric susceptibility (≈ by a factor of 2) and the piezoelectric constants, reflecting the strong anharmonicity of this ferroelectric system even at very low temperature. The slow temperature-evolution of the dielectric properties observed below ≈100 K is attributed (i) to zero-point energy contributions and (ii) to harmonic behavior if the quantum effects are turned off.
Isotope effects in water as investigated by neutron diffraction and path integral molecular dynamics
NASA Astrophysics Data System (ADS)
Zeidler, Anita; Salmon, Philip S.; Fischer, Henry E.; Neuefeind, Jörg C.; Simonson, J. Mike; Markland, Thomas E.
2012-07-01
The structures of heavy and light water at 300 K were investigated by using a joint approach in which the method of neutron diffraction with oxygen isotope substitution was complemented by path integral molecular dynamics simulations. The diffraction results, which give intra-molecular O-D and O-H bond distances of 0.985(5) and 0.990(5) Å, were found to be in best agreement with those obtained by using the flexible anharmonic TTM3-F water model. Both techniques show a difference of ≃ 0.5% between the O-D and O-H intra-molecular bond lengths, and the results support a competing quantum effects model for water in which its structural and dynamical properties are governed by an offset between intra-molecular and inter-molecular quantum contributions. Further consideration of the O-O correlations is needed in order to improve agreement with experiment.
Path Integral Monte Carlo and Density Functional Molecular Dynamics Simulations of Warm Dense Matter
NASA Astrophysics Data System (ADS)
Militzer, Burkhard; Driver, Kevin
2011-10-01
We analyze the applicability of two first-principles simulation techniques, path integral Monte Carlo (PIMC) and density functional molecular dynamics (DFT-MD), to study the regime of warm dense matter. We discuss the advantages as well as the limitations of each method and propose directions for future development. Results for dense, liquid helium, where both methods have been applied, demonstrate the range of each method's applicability. Comparison of the equations of state from simulations with analytical theories and free energy models show that DFT is useful for temperatures below 100000 K and then PIMC provides accurate results for all higher temperatures. We characterize the structure of the liquid in terms of pair correlation functions and study the closure of the band gap with increasing density and temperature. Finally, we discuss simulations of heavier elements and demonstrate the reliability are both methods in such cases with preliminary results.
NASA Technical Reports Server (NTRS)
Singh, Upendra N.; Yu, Jirong; Petros, Mulugeta; Refaat, Tamer F.; Remus, Ruben G.; Fay, James J.; Reithmaier, Karl
2014-01-01
Double-pulse 2-micron lasers have been demonstrated with energy as high as 600 millijouls and up to 10 Hz repetition rate. The two laser pulses are separated by 200 microseconds and can be tuned and locked separately. Applying double-pulse laser in DIAL system enhances the CO2 measurement capability by increasing the overlap of the sampled volume between the on-line and off-line. To avoid detection complicity, integrated path differential absorption (IPDA) lidar provides higher signal-to-noise ratio measurement compared to conventional range-resolved DIAL. Rather than weak atmospheric scattering returns, IPDA rely on the much stronger hard target returns that is best suited for airborne platforms. In addition, the IPDA technique measures the total integrated column content from the instrument to the hard target but with weighting that can be tuned by the transmitter. Therefore, the transmitter could be tuned to weight the column measurement to the surface for optimum CO2 interaction studies or up to the free troposphere for optimum transport studies. Currently, NASA LaRC is developing and integrating a double-Pulsed 2-micron direct detection IPDA lidar for CO2 column measurement from an airborne platform. The presentation will describe the development of the 2-micron IPDA lidar system and present the airborne measurement of column CO2 and will compare to in-situ measurement for various ground target of different reflectivity.
NASA Astrophysics Data System (ADS)
Singh, Upendra N.; Yu, Jirong; Petros, Mulugeta; Refaat, Tamer F.; Remus, Ruben G.; Fay, James J.; Reithmaier, Karl
2014-10-01
Double-pulse 2-micron lasers have been demonstrated with energy as high as 600 mJ and up to 10 Hz repetition rate. The two laser pulses are separated by 200 µs and can be tuned and locked separately. Applying double-pulse laser in DIAL system enhances the CO2 measurement capability by increasing the overlap of the sampled volume between the on-line and off-line. To avoid detection complicity, integrated path differential absorption (IPDA) lidar provides higher signal-to-noise ratio measurement compared to conventional range-resolved DIAL. Rather than weak atmospheric scattering returns, IPDA rely on the much stronger hard target returns that is best suited for airborne platforms. In addition, the IPDA technique measures the total integrated column content from the instrument to the hard target but with weighting that can be tuned by the transmitter. Therefore, the transmitter could be tuned to weight the column measurement to the surface for optimum CO2 interaction studies or up to the free troposphere for optimum transport studies. Currently, NASA LaRC is developing and integrating a double-Pulsed 2-µm direct detection IPDA lidar for CO2 column measurement from an airborne platform. The presentation will describe the development of the 2-μm IPDA lidar system and present the airborne measurement of column CO2 and will compare to in-situ measurement for various ground target of different reflectivity.
Maintaining a cognitive map in darkness: the need to fuse boundary knowledge with path integration.
Cheung, Allen; Ball, David; Milford, Michael; Wyeth, Gordon; Wiles, Janet
2012-01-01
Spatial navigation requires the processing of complex, disparate and often ambiguous sensory data. The neurocomputations underpinning this vital ability remain poorly understood. Controversy remains as to whether multimodal sensory information must be combined into a unified representation, consistent with Tolman's "cognitive map", or whether differential activation of independent navigation modules suffice to explain observed navigation behaviour. Here we demonstrate that key neural correlates of spatial navigation in darkness cannot be explained if the path integration system acted independently of boundary (landmark) information. In vivo recordings demonstrate that the rodent head direction (HD) system becomes unstable within three minutes without vision. In contrast, rodents maintain stable place fields and grid fields for over half an hour without vision. Using a simple HD error model, we show analytically that idiothetic path integration (iPI) alone cannot be used to maintain any stable place representation beyond two to three minutes. We then use a measure of place stability based on information theoretic principles to prove that featureless boundaries alone cannot be used to improve localization above chance level. Having shown that neither iPI nor boundaries alone are sufficient, we then address the question of whether their combination is sufficient and--we conjecture--necessary to maintain place stability for prolonged periods without vision. We addressed this question in simulations and robot experiments using a navigation model comprising of a particle filter and boundary map. The model replicates published experimental results on place field and grid field stability without vision, and makes testable predictions including place field splitting and grid field rescaling if the true arena geometry differs from the acquired boundary map. We discuss our findings in light of current theories of animal navigation and neuronal computation, and elaborate on
Fermionic path-integral Monte Carlo results for the uniform electron gas at finite temperature.
Filinov, V S; Fortov, V E; Bonitz, M; Moldabekov, Zh
2015-03-01
The uniform electron gas (UEG) at finite temperature has recently attracted substantial interest due to the experimental progress in the field of warm dense matter. To explain the experimental data, accurate theoretical models for high-density plasmas are needed that depend crucially on the quality of the thermodynamic properties of the quantum degenerate nonideal electrons and of the treatment of their interaction with the positive background. Recent fixed-node path-integral Monte Carlo (RPIMC) data are believed to be the most accurate for the UEG at finite temperature, but they become questionable at high degeneracy when the Brueckner parameter rs=a/aB--the ratio of the mean interparticle distance to the Bohr radius--approaches 1. The validity range of these simulations and their predictive capabilities for the UEG are presently unknown. This is due to the unknown quality of the used fixed nodes and of the finite-size scaling from N=33 simulated particles (per spin projection) to the macroscopic limit. To analyze these questions, we present alternative direct fermionic path integral Monte Carlo (DPIMC) simulations that are independent from RPIMC. Our simulations take into account quantum effects not only in the electron system but also in their interaction with the uniform positive background. Also, we use substantially larger particle numbers (up to three times more) and perform an extrapolation to the macroscopic limit. We observe very good agreement with RPIMC, for the polarized electron gas, up to moderate densities around rs=4, and larger deviations for the unpolarized case, for low temperatures. For higher densities (high electron degeneracy), rs≲1.5, both RPIMC and DPIMC are problematic due to the increased fermion sign problem.
Fine, Dana S.; Sawin, Stephen
2014-06-15
Following Feynman's prescription for constructing a path integral representation of the propagator of a quantum theory, a short-time approximation to the propagator for imaginary-time, N = 1 supersymmetric quantum mechanics on a compact, even-dimensional Riemannian manifold is constructed. The path integral is interpreted as the limit of products, determined by a partition of a finite time interval, of this approximate propagator. The limit under refinements of the partition is shown to converge uniformly to the heat kernel for the Laplace-de Rham operator on forms. A version of the steepest descent approximation to the path integral is obtained, and shown to give the expected short-time behavior of the supertrace of the heat kernel.
Song, Linze; Shi, Qiang
2015-05-07
We present a new non-perturbative method to calculate the charge carrier mobility using the imaginary time path integral approach, which is based on the Kubo formula for the conductivity, and a saddle point approximation to perform the analytic continuation. The new method is first tested using a benchmark calculation from the numerical exact hierarchical equations of motion method. Imaginary time path integral Monte Carlo simulations are then performed to explore the temperature dependence of charge carrier delocalization and mobility in organic molecular crystals (OMCs) within the Holstein and Holstein-Peierls models. The effects of nonlocal electron-phonon interaction on mobility in different charge transport regimes are also investigated.
Causo, Maria Serena; Ciccotti, Giovanni; Montemayor, Daniel; Bonella, Sara; Coker, David F
2005-04-14
We generalize the linearized path integral approach to evaluate quantum time correlation functions for systems best described by a set of nuclear and electronic degrees of freedom, restricting ourselves to the adiabatic approximation. If the operators in the correlation function are nondiagonal in the electronic states, then this adiabatic linearized path integral approximation for the thermal averaged quantum dynamics presents interesting and distinctive features, which we derive and explore in this paper. The capability of these approximations to accurately reproduce the behavior of physical systems is demonstrated by calculating the diffusion constant for an excess electron in a metal-molten salt solution.
NASA Astrophysics Data System (ADS)
Fishman, Louis
2000-11-01
The role of mathematical modeling in the physical sciences will be briefly addressed. Examples will focus on computational acoustics, with applications to underwater sound propagation, electromagnetic modeling, optics, and seismic inversion. Direct and inverse wave propagation problems in both the time and frequency domains will be considered. Focusing on fixed-frequency (elliptic) wave propagation problems, the usual, two-way, partial differential equation formulation will be exactly reformulated, in a well-posed manner, as a one-way (marching) problem. This is advantageous for both direct and inverse considerations, as well as stochastic modeling problems. The reformulation will require the introduction of pseudodifferential operators and their accompanying phase space analysis (calculus), in addition to path integral representations for the fundamental solutions and their subsequent computational algorithms. Unlike the more traditional, purely numerical applications of, for example, finite-difference and finite-element methods, this approach, in effect, writes the exact, or, more generally, the asymptotically correct, answer as a functional integral and, subsequently, computes it directly. The overall computational philosophy is to combine analysis, asymptotics, and numerical methods to attack complicated, real-world problems. Exact and asymptotic analysis will stress the complementary nature of the direct and inverse formulations, as well as indicating the explicit structural connections between the time- and frequency-domain solutions.
Path integral calculation of free energies: quantum effects on the melting temperature of neon.
Ramírez, R; Herrero, C P; Antonelli, A; Hernández, E R
2008-08-14
The path integral formulation has been combined with several methods to determine free energies of quantum many-body systems, such as adiabatic switching and reversible scaling. These techniques are alternatives to the standard thermodynamic integration method. A quantum Einstein crystal is used as a model to demonstrate the accuracy and reliability of these free energy methods in quantum simulations. Our main interest focuses on the calculation of the melting temperature of Ne at ambient pressure, taking into account quantum effects in the atomic dynamics. The free energy of the solid was calculated by considering a quantum Einstein crystal as reference state, while for the liquid, the reference state was defined by the classical limit of the fluid. Our findings indicate that, while quantum effects in the melting temperature of this system are small, they still amount to about 6% of the melting temperature, and are therefore not negligible. The particle density as well as the melting enthalpy and entropy of the solid and liquid phases at coexistence is compared to results obtained in the classical limit and also to available experimental data.
Ab initio path-integral molecular dynamics and the quantum nature of hydrogen bonds
NASA Astrophysics Data System (ADS)
Yexin, Feng; Ji, Chen; Xin-Zheng, Li; Enge, Wang
2016-01-01
The hydrogen bond (HB) is an important type of intermolecular interaction, which is generally weak, ubiquitous, and essential to life on earth. The small mass of hydrogen means that many properties of HBs are quantum mechanical in nature. In recent years, because of the development of computer simulation methods and computational power, the influence of nuclear quantum effects (NQEs) on the structural and energetic properties of some hydrogen bonded systems has been intensively studied. Here, we present a review of these studies by focussing on the explanation of the principles underlying the simulation methods, i.e., the ab initio path-integral molecular dynamics. Its extension in combination with the thermodynamic integration method for the calculation of free energies will also be introduced. We use two examples to show how this influence of NQEs in realistic systems is simulated in practice. Project supported by the National Natural Science Foundation of China (Grant Nos. 11275008, 91021007, and 10974012) and the China Postdoctoral Science Foundation (Grant No. 2014M550005).
NASA Technical Reports Server (NTRS)
Singh, Upendra N.; Refaat, Tamer F.; Petros, Mulugeta; Yu, Jirong
2015-01-01
The two-micron wavelength is suitable for monitoring atmospheric water vapor and carbon dioxide, the two most dominant greenhouse gases. Recent advances in 2-micron laser technology paved the way for constructing state-of-the-art lidar transmitters for active remote sensing applications. In this paper, a new triple-pulsed 2-micron integrated path differential absorption lidar is presented. This lidar is capable of measuring either two species or single specie with two different weighting functions, simultaneously and independently. Development of this instrument is conducted at NASA Langley Research Center. Instrument scaling for projected future space missions will be discussed.
Wong, Kin-Yiu; Xu, Yuqing; Xu, Liang
2015-11-01
Enzymatic reactions are integral components in many biological functions and malfunctions. The iconic structure of each reaction path for elucidating the reaction mechanism in details is the molecular structure of the rate-limiting transition state (RLTS). But RLTS is very hard to get caught or to get visualized by experimentalists. In spite of the lack of explicit molecular structure of the RLTS in experiment, we still can trace out the RLTS unique "fingerprints" by measuring the isotope effects on the reaction rate. This set of "fingerprints" is considered as a most direct probe of RLTS. By contrast, for computer simulations, oftentimes molecular structures of a number of TS can be precisely visualized on computer screen, however, theoreticians are not sure which TS is the actual rate-limiting one. As a result, this is an excellent stage setting for a perfect "marriage" between experiment and theory for determining the structure of RLTS, along with the reaction mechanism, i.e., experimentalists are responsible for "fingerprinting", whereas theoreticians are responsible for providing candidates that match the "fingerprints". In this Review, the origin of isotope effects on a chemical reaction is discussed from the perspectives of classical and quantum worlds, respectively (e.g., the origins of the inverse kinetic isotope effects and all the equilibrium isotope effects are purely from quantum). The conventional Bigeleisen equation for isotope effect calculations, as well as its refined version in the framework of Feynman's path integral and Kleinert's variational perturbation (KP) theory for systematically incorporating anharmonicity and (non-parabolic) quantum tunneling, are also presented. In addition, the outstanding interplay between theory and experiment for successfully deducing the RLTS structures and the reaction mechanisms is demonstrated by applications on biochemical reactions, namely models of bacterial squalene-to-hopene polycyclization and RNA 2'-O
Emissions of ammonia and methane from an anaerobic lagoon at a swine animal feeding operation were evaluated five times over a period of two years. The plane-integrated (PI) open-path Fourier transform infrared spectrometry (OP-FTIR) methodology was used to transect the plume at ...
Kleinert, H; Zatloukal, V
2013-11-01
The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.
Grinberg, H.; Maranon, J.; Vucetich, H.
1983-01-15
The Kustaanheimo--Stiefel transformation together with the well-known expansion of the kernel of an isotropic harmonic oscillator is used to generate the atomic orbitals of the nonrelativistic hydrogen atom in a four-dimensional Riemann space through the path integral formalism. Group theoretical implications of the present problem are briefly discussed.
Botelho, L.C.L.
1985-03-15
We study a two-dimensional quantum field model with axial-vector-current--pseudoscalar derivative interaction using path-integral methods. We construct an effective Lagrangian by performing a chiral change in the fermionic variables leading to an exact solution of the model.
ERIC Educational Resources Information Center
Field, J. H.
2011-01-01
It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…
Wiese, Kay Jörg
2016-04-01
We derive and study two different formalisms used for nonequilibrium processes: the coherent-state path integral, and an effective, coarse-grained stochastic equation of motion. We first study the coherent-state path integral and the corresponding field theory, using the annihilation process A+A→A as an example. The field theory contains counterintuitive quartic vertices. We show how they can be interpreted in terms of a first-passage problem. Reformulating the coherent-state path integral as a stochastic equation of motion, the noise generically becomes imaginary. This renders it not only difficult to interpret, but leads to convergence problems at finite times. We then show how alternatively an effective coarse-grained stochastic equation of motion with real noise can be constructed. The procedure is similar in spirit to the derivation of the mean-field approximation for the Ising model, and the ensuing construction of its effective field theory. We finally apply our findings to stochastic Manna sandpiles. We show that the coherent-state path integral is inappropriate, or at least inconvenient. As an alternative, we derive and solve its mean-field approximation, which we then use to construct a coarse-grained stochastic equation of motion with real noise.
ERIC Educational Resources Information Center
Miller, Melvin E., Ed.; Cook-Greuter, Susanne R., Ed.
This book contains 11 papers on creativity, spirituality, and transcendence as paths to integrity and wisdom in the mature self. The book begins with the paper "Introduction--Creativity in Adulthood: Personal Maturity and Openness to Extraordinary Sources of Inspiration" (Susanne R. Cook-Greuter, Melvin E. Miller). The next four papers,…
NASA Astrophysics Data System (ADS)
Shiga, Motoyuki; Tachikawa, Masanori; Miura, Shinichi
2000-12-01
We present an accurate calculational scheme for many-body systems composed of electrons and nuclei, by path integral molecular dynamics technique combined with the ab initio molecular orbital theory. Based upon the scheme, the simulation of a water molecule at room temperature is demonstrated, applying all-electron calculation at the Hartree-Fock level of theory.
Moving to a Soft Path for Water: Integrated Research and Management Needs
NASA Astrophysics Data System (ADS)
Gleick, P. H.
2011-12-01
Water on Earth in its three fundamental phases is integral to the functioning, dynamics, and variability of the global climatological and biological support systems. From a purely scientific point of view, understanding the complexity of the hydrological cycle is of paramount interest and central to our understanding of other planetary geological, atmospheric, chemical, and physical processes. But water is more than that: water is key to economic, social, and political issues as well, including some of the core challenges of our time such central to issues of poverty, health, environmental sustainability, conflict, and economic prosperity. The more society seeks to solve these challenges, the more obvious it becomes that we must improve more than just our understanding of the fundamental science of the hydrological cycle and its links with related global processes; we must also improve our understanding of the complex social, economic, and structural challenges facing water managers and users. We must move to a different paradigm where water is managed in a far more integrated way - what I call the "soft path for water." Central to our basic science needs are (1) an expansion of the frequency and nature of the data we collect, (2) the development of systems for managing, sharing, and analyzing those data, and (3) improvements in our ability to model and forecast the hydrological cycle together with other climatological, geophysical, and biochemical systems. These improvements would lead to a far better understanding of the local, regional, and global details of the water balance on timescales from minutes to millennia. These needs are increasingly well understood in the research community and extensive efforts in these areas are underway under the auspices of national research centers, universities, and international scientific collaborations. But it is also becoming increasingly apparent that many of the current water challenges facing society are not going to be
Path Integral Monte Carlo finite-temperature electronic structure of quantum dots
NASA Astrophysics Data System (ADS)
Leino, Markku; Rantala, Tapio T.
2003-03-01
Quantum Monte Carlo methods allow a straightforward procedure for evaluation of electronic structures with a proper treatment of electronic correlations. This can be done even at finite temperatures [1]. We apply the Path Integral Monte Carlo (PIMC) simulation method [2] for one and two electrons in a single and double quantum dots. With this approach we evaluate the electronic distributions and correlations, and finite temperature effects on those. Temperature increase broadens the one-electron distribution as expected. This effect is smaller for correlated electrons than for single ones. The simulated one and two electron distributions of a single and two coupled quantum dots are also compared to those from experiments and other theoretical (0 K) methods [3]. Computational capacity is found to become the limiting factor in simulations with increasing accuracy. This and other essential aspects of PIMC and its capability in this type of calculations are also discussed. [1] R.P. Feynman: Statistical Mechanics, Addison Wesley, 1972. [2] D.M. Ceperley, Rev.Mod.Phys. 67, 279 (1995). [3] M. Pi, A. Emperador and M. Barranco, Phys.Rev.B 63, 115316 (2001).
Neural Network-Based Solutions for Stochastic Optimal Control Using Path Integrals.
Rajagopal, Karthikeyan; Balakrishnan, Sivasubramanya Nadar; Busemeyer, Jerome R
2017-03-01
In this paper, an offline approximate dynamic programming approach using neural networks is proposed for solving a class of finite horizon stochastic optimal control problems. There are two approaches available in the literature, one based on stochastic maximum principle (SMP) formalism and the other based on solving the stochastic Hamilton-Jacobi-Bellman (HJB) equation. However, in the presence of noise, the SMP formalism becomes complex and results in having to solve a couple of backward stochastic differential equations. Hence, current solution methodologies typically ignore the noise effect. On the other hand, the inclusion of noise in the HJB framework is very straightforward. Furthermore, the stochastic HJB equation of a control-affine nonlinear stochastic system with a quadratic control cost function and an arbitrary state cost function can be formulated as a path integral (PI) problem. However, due to curse of dimensionality, it might not be possible to utilize the PI formulation for obtaining comprehensive solutions over the entire operating domain. A neural network structure called the adaptive critic design paradigm is used to effectively handle this difficulty. In this paper, a novel adaptive critic approach using the PI formulation is proposed for solving stochastic optimal control problems. The potential of the algorithm is demonstrated through simulation results from a couple of benchmark problems.
Exact path-integral evaluation of the heat distribution function of a trapped Brownian oscillator
NASA Astrophysics Data System (ADS)
Chatterjee, Debarati; Cherayil, Binny J.
2010-11-01
Using path integrals, we derive an exact expression—valid at all times t —for the distribution P(Q,t) of the heat fluctuations Q of a Brownian particle trapped in a stationary harmonic well. We find that P(Q,t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t→∞ exactly recovers the heat distribution function obtained recently by Imparato [Phys. Rev. E 76, 050101(R) (2007)]10.1103/PhysRevE.76.050101 from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen [Phys. Rev. E 69, 056121 (2004)]10.1103/PhysRevE.69.056121; however, this calculation does not provide an expression for P(Q,t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P(Q,t) for the case v=0 .
A new approach to gravitational clustering: A path-integral formalism and large-N expansions
NASA Astrophysics Data System (ADS)
Valageas, P.
2004-07-01
We show that the formation of large-scale structures through gravitational instability in the expanding universe can be fully described through a path-integral formalism. We derive the action S[f] which gives the statistical weight associated with any phase-space distribution function f({x},{p},t). This action S describes both the average over the Gaussian initial conditions and the Vlasov-Poisson dynamics. Next, applying a standard method borrowed from field theory we generalize our problem to an N-field system and we look for an expansion over powers of 1/N. We describe three such methods and we derive the corresponding equations of motion at the lowest non-trivial order for the case of gravitational clustering. This yields a set of non-linear equations for the mean /line{f} and the two-point correlation G of the phase-space distribution f, as well as for the response function R. These systematic schemes match the usual perturbative expansion on quasi-linear scales but should also be able to treat the non-linear regime. Our approach can also be extended to non-Gaussian initial conditions and may serve as a basis for other tools borrowed from field theory. Appendix A is only available in electronic form at http://www.edpsciences.org
Path-integral simulation of ice VII: Pressure and temperature effects
NASA Astrophysics Data System (ADS)
Herrero, Carlos P.; Ramírez, Rafael
2015-11-01
The effects of pressure and temperature on structural and thermodynamic properties of ice VII have been studied by using path-integral molecular dynamics (PIMD) simulations. Temperatures between 25 and 450 K, as well as pressures up to 12 GPa were considered. Interatomic interactions were modeled by using the effective q-TIP4P/F potential for flexible water. We analyze the pressure dependence of the molar volume, bulk modulus, interatomic distances, kinetic energy, and atomic delocalization at various temperatures. Results of PIMD simulations are compared with those derived from a quasi-harmonic approximation (QHA) of vibrational modes, which helps to assess the importance of anharmonic effects, as well as the influence of the different modes on the properties of ice VII. The accuracy of the QHA for describing this high-pressure phase decreases for rising temperature, but this approximation becomes more reliable as pressure grows, since anharmonicity becomes less relevant. Comparisons with low-pressure cubic ice are presented.
A path-integral Monte Carlo study of a small cluster: The Ar trimer
NASA Astrophysics Data System (ADS)
Pérez de Tudela, R.; Márquez-Mijares, M.; González-Lezana, T.; Roncero, O.; Miret-Artés, S.; Delgado-Barrio, G.; Villarreal, P.
2010-06-01
The Ar3 system has been studied between T =0 K and T =40 K by means of a path-integral Monte Carlo (PIMC) method. The behavior of the average energy in terms of the temperature has been explained by comparison with results obtained with the thermal averaged rovibrational spectra estimated via: (i) a quantum mechanical method based on distributed Gaussian functions for the interparticle distances and (ii) an analytical model which precisely accounts for the participation of the dissociative continua Ar2+Ar and Ar+Ar+Ar. Beyond T ˜20 K, the system explores floppier configurations than the rigid equilateral geometry, as linear and Ar-Ar2-like arrangements, and fragmentates around T ˜40 K. A careful investigation of the specific heat in terms of a confining radius in the PIMC calculation seems to discard a proper phase transition as in larger clusters, in apparent contradiction with previous reports of precise values for a liquid-gas transition. The onset of this noticeable change in the dynamics of the trimer occurs, however, at a remarkably low value of the temperature in comparison with Arn systems formed with more Ar atoms. Quantum mechanical effects are found of relevance at T ≤15 K, with both energies and radial distributions obtained with a quantum PIMC deviating from the corresponding classical results, thus precluding exclusively classical approaches for a precise description of the system at this low temperature range.
NASA Astrophysics Data System (ADS)
Sesé, Luis M.
2017-02-01
This work deals with the computation of the structure factors of quantum fluids under complex conditions involving substantial density fluctuations and/or large particle delocalization effects. The method is based on the combination of path-integral Monte Carlo (PIMC) simulations and the pair Ornstein-Zernike framework (OZ2). PIMC provides the radial correlation functions (centroid, instantaneous, and thermalized-continuous total linear response), which are used as data input to the OZ2 calculations that lead to their associated structure factors. To undertake this project normal liquid 4He and supercritical 3He are selected, studying conditions in the range (T = 4.2 K; 0.01886 <ρN/Å-3 < 0.02687). Full inter-comparison between the structure factors determined via both OZ2 and direct PIMC calculations is made. In addition, comparison with experimental data, including thermodynamic properties, is made wherever possible. The results establish that, even under severe thermodynamic and/or quantum fluctuation conditions, OZ2 remains in the quantum domain as a highly reliable and cost-effective framework to determine accurate structure factors, also allowing one to understand the related isotopic shifts in fluid He.
NASA Astrophysics Data System (ADS)
Tachikawa, Masanori; Shiga, Motoyuki
2004-09-01
We have applied the ab initio path integral molecular dynamics simulation to study hydronium ion and its isotopes, which are the simplest systems for hydrated proton and deuteron. In this simulation, all the rotational and vibrational degrees of freedom are treated fully quantum mechanically, while the potential energies of the respective atomic configurations are calculated "on the fly" using ab initio quantum chemical approach. With the careful treatment of the ab initio electronic structure calculation by relevant choices in electron correlation level and basis set, this scheme is theoretically quite rigorous except for Born-Oppenheimer approximation. This accurate calculation allows a close insight into the structural shifts for the isotopes of hydronium ion by taking account of both quantum mechanical and thermal effects. In fact, the calculation is shown to be successful to quantitatively extract the geometrical isotope effect with respect to the Walden inversion. It is also shown that this leads to the isotope effect on the electronic structure as well as the thermochemical properties.
NASA Astrophysics Data System (ADS)
Liu, Bing-Yi; Wang, Jun-Yang; Liu, Zhi-Shen
2014-11-01
Spaceborne integrated path differential absorption (IPDA) lidar is an active-detection system which is able to perform global CO2 measurement with high accuracy of 1ppmv at day and night over ground and clouds. To evaluate the detection performance of the system, simulation of the ground return signal and retrieval algorithm for CO2 concentration are presented in this paper. Ground return signals of spaceborne IPDA lidar under various ground surface reflectivity and atmospheric aerosol optical depths are simulated using given system parameters, standard atmosphere profiles and HITRAN database, which can be used as reference for determining system parameters. The simulated signals are further applied to the research on retrieval algorithm for CO2 concentration. The column-weighted dry air mixing ratio of CO2 denoted by XCO2 is obtained. As the deviations of XCO2 between the initial values for simulation and the results from retrieval algorithm are within the expected error ranges, it is proved that the simulation and retrieval algorithm are reliable.
Bayesian Uncertainty Quantification for Bond Energies and Mobilities Using Path Integral Analysis
Chang, Joshua C.; Fok, Pak-Wing; Chou, Tom
2015-01-01
Dynamic single-molecule force spectroscopy is often used to distort bonds. The resulting responses, in the form of rupture forces, work applied, and trajectories of displacements, are used to reconstruct bond potentials. Such approaches often rely on simple parameterizations of one-dimensional bond potentials, assumptions on equilibrium starting states, and/or large amounts of trajectory data. Parametric approaches typically fail at inferring complicated bond potentials with multiple minima, while piecewise estimation may not guarantee smooth results with the appropriate behavior at large distances. Existing techniques, particularly those based on work theorems, also do not address spatial variations in the diffusivity that may arise from spatially inhomogeneous coupling to other degrees of freedom in the macromolecule. To address these challenges, we develop a comprehensive empirical Bayesian approach that incorporates data and regularization terms directly into a path integral. All experimental and statistical parameters in our method are estimated directly from the data. Upon testing our method on simulated data, our regularized approach requires less data and allows simultaneous inference of both complex bond potentials and diffusivity profiles. Crucially, we show that the accuracy of the reconstructed bond potential is sensitive to the spatially varying diffusivity and accurate reconstruction can be expected only when both are simultaneously inferred. Moreover, after providing a means for self-consistently choosing regularization parameters from data, we derive posterior probability distributions, allowing for uncertainty quantification. PMID:26331254
Iterative quantum-classical path integral with dynamically consistent state hopping
Walters, Peter L.; Makri, Nancy
2016-01-28
We investigate the convergence of iterative quantum-classical path integral calculations in sluggish environments strongly coupled to a quantum system. The number of classical trajectories, thus the computational cost, grows rapidly (exponentially, unless filtering techniques are employed) with the memory length included in the calculation. We argue that the choice of the (single) trajectory branch during the time preceding the memory interval can significantly affect the memory length required for convergence. At short times, the trajectory branch associated with the reactant state improves convergence by eliminating spurious memory. We also introduce an instantaneous population-based probabilistic scheme which introduces state-to-state hops in the retained pre-memory trajectory branch, and which is designed to choose primarily the trajectory branch associated with the reactant at early times, but to favor the product state more as the reaction progresses to completion. Test calculations show that the dynamically consistent state hopping scheme leads to accelerated convergence and a dramatic reduction of computational effort.
Path Integral Monte Carlo Simulations of Warm Dense Plasmas with mid-Z Elements
NASA Astrophysics Data System (ADS)
Driver, Kevin; Soubiran, Francois; Zhang, Shuai; Militzer, Burkhard
2016-10-01
Theoretical studies of warm dense plasmas are crucial for improving our knowledge of giant planets, astrophysics, shock physics, and new plasma energy technologies, such as inertial confined fusion. Path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) provide consistent, first-principles descriptions of warm, dense matter over a wide range of density and temperature conditions. Here, we report simulation results for a variety of first- and second-row elements. DFT-MD algorithms are well-suited for low temperatures, while PIMC has been restricted to relatively high temperatures due to the free-particle approximation of the nodal surface. For heavier, second-row elements, we have developed a new, localized nodal surface, which allows us to treat bound states within the PIMC formalism. By combining PIMC and DFT-MD pressures and internal energies, we produce a coherent, first-principles equation of state, bridging the entire warm dense matter regime. Pair-correlation functions and the density of electronic states reveal an evolving plasma structure. The degree of ionization is affected by both temperature and density. Finally, shock Hugoniot curves show an increase in compression as the first and second shells are ionized. Funding provided by the DOE (DE-SC0010517). Computational resources provided by the NCAR/CISL, NERSC, and NASA.
The quantum nature of the hydrogen bond: insight from path-integral molecular dynamics
NASA Astrophysics Data System (ADS)
Walker, Brent; Li, Xin-Zheng; Michaelides, Angelos
2011-03-01
Hydrogen (H) bonds are weak, generally intermolecular bonds, that hold together much of soft matter, the condensed phases of water, network liquids, and many ferroelectric crystals. The small mass of H means H-bonds are inherently quantum mechanical; effects such as zero point motion and tunneling should be considered, although often are not. In particular, a consistent picture of quantum nuclear effects on the strength of H-bonds and consequently the structure of H-bonded systems is still absent. Here, we report ab initio path-integral molecular dynamics studies on the quantum nature of the H-bond. Systematic examination of a range of H-bonded systems shows that quantum nuclei weaken weak H-bonds but strengthen relatively strong ones. This correlation arises from a competition between anharmonic intermolecular bond bending and intramolecular bond stretching. A simple rule of thumb enables predictions to be made for H-bonded bonded materials in general with merely classical knowledge (e.g. H-bond strength or H-bond length). Our work rationalizes the contrasting influence of quantum nuclear dynamics on a wide variety of materials, including liquid water and HF, and highlights the need for flexible molecules in force-field based studies of quantum nuclear dynamics.
NASA Astrophysics Data System (ADS)
Mühlbacher, Lothar; Ankerhold, Joachim
2005-05-01
Electron transfer (ET) across molecular chains including an impurity is studied based on a recently improved real-time path-integral Monte Carlo (PIMC) approach [L. Mühlbacher, J. Ankerhold, and C. Escher, J. Chem. Phys. 121 12696 (2004)]. The reduced electronic dynamics is studied for various bridge lengths and defect site energies. By determining intersite hopping rates from PIMC simulations up to moderate times, the relaxation process in the extreme long-time limit is captured within a sequential transfer model. The total transfer rate is extracted and shown to be enhanced for certain defect site energies. Superexchange turns out to be relevant for extreme gap energies only and then gives rise to different dynamical signatures for high- and low-lying defects. Further, it is revealed that the entire bridge compound approaches a steady state on a much shorter time scale than that related to the total transfer. This allows for a simplified description of ET along donor-bridge-acceptor systems in the long-time range.
Path integral Monte Carlo and density functional molecular dynamics simulations of hot, dense helium
NASA Astrophysics Data System (ADS)
Militzer, B.
2009-04-01
Two first-principles simulation techniques, path integral Monte Carlo (PIMC) and density functional molecular dynamics (DFT-MD), are applied to study hot, dense helium in the density-temperature range of 0.387-5.35gcm-3 and 500K-1.28×108K . One coherent equation of state is derived by combining DFT-MD data at lower temperatures with PIMC results at higher temperatures. Good agreement between both techniques is found in an intermediate-temperature range. For the highest temperatures, the PIMC results converge to the Debye-Hückel limiting law. In order to derive the entropy, a thermodynamically consistent free-energy fit is used that reproduces the internal energies and pressure derived from the first-principles simulations. The equation of state is presented in the form of a table as well as a fit and is compared with different free-energy models. Pair-correlation functions and the electronic density of states are discussed. Shock Hugoniot curves are compared with recent laser shock-wave experiments.
Path-integral molecular dynamics simulation of 3C-SiC
NASA Astrophysics Data System (ADS)
Ramírez, Rafael; Herrero, Carlos P.; Hernández, Eduardo R.; Cardona, Manuel
2008-01-01
Molecular dynamics simulations of 3C-SiC have been performed as a function of pressure and temperature. These simulations treat both electrons and atomic nuclei by quantum mechanical methods. While the electronic structure of the solid is described by an efficient tight-binding Hamiltonian, the nuclei dynamics is treated by the path-integral formulation of statistical mechanics. To assess the relevance of nuclear quantum effects, the results of quantum simulations are compared to others where either the Si nuclei, the C nuclei, or both atomic nuclei are treated as classical particles. We find that the experimental thermal expansion of 3C-SiC is realistically reproduced by our simulations. The calculated bulk modulus of 3C-SiC and its pressure derivative at room temperature show also good agreement with the available experimental data. The effect of the electron-phonon interaction on the direct electronic gap of 3C-SiC has been calculated as a function of temperature and related to results obtained for bulk diamond and Si. Comparison to available experimental data shows satisfactory agreement, although we observe that the employed tight-binding model tends to overestimate the magnitude of the electron-phonon interaction. The effect of treating the atomic nuclei as classical particles on the direct gap of 3C-SiC has been assessed. We find that nonlinear quantum effects related to the atomic masses are particularly relevant at temperatures below 250K .
Path integration and cognitive mapping in a continuous attractor neural network model.
Samsonovich, A; McNaughton, B L
1997-08-01
A minimal synaptic architecture is proposed for how the brain might perform path integration by computing the next internal representation of self-location from the current representation and from the perceived velocity of motion. In the model, a place-cell assembly called a "chart" contains a two-dimensional attractor set called an "attractor map" that can be used to represent coordinates in any arbitrary environment, once associative binding has occurred between chart locations and sensory inputs. In hippocampus, there are different spatial relations among place fields in different environments and behavioral contexts. Thus, the same units may participate in many charts, and it is shown that the number of uncorrelated charts that can be encoded in the same recurrent network is potentially quite large. According to this theory, the firing of a given place cell is primarily a cooperative effect of the activity of its neighbors on the currently active chart. Therefore, it is not particularly useful to think of place cells as encoding any particular external object or event. Because of its recurrent connections, hippocampal field CA3 is proposed as a possible location for this "multichart" architecture; however, other implementations in anatomy would not invalidate the main concepts. The model is implemented numerically both as a network of integrate-and-fire units and as a "macroscopic" (with respect to the space of states) description of the system, based on a continuous approximation defined by a system of stochastic differential equations. It provides an explanation for a number of hitherto perplexing observations on hippocampal place fields, including doubling, vanishing, reshaping in distorted environments, acquiring directionality in a two-goal shuttling task, rapid formation in a novel environment, and slow rotation after disorientation. The model makes several new predictions about the expected properties of hippocampal place cells and other cells of the
Equilibrium fractionation of H and O isotopes in water from path integral molecular dynamics
NASA Astrophysics Data System (ADS)
Pinilla, Carlos; Blanchard, Marc; Balan, Etienne; Ferlat, Guillaume; Vuilleumier, Rodolphe; Mauri, Francesco
2014-06-01
The equilibrium fractionation factor between two phases is of importance for the understanding of many planetary and environmental processes. Although thermodynamic equilibrium can be achieved between minerals at high temperature, many natural processes involve reactions between liquids or aqueous solutions and solids. For crystals, the fractionation factor α can be theoretically determined using a statistical thermodynamic approach based on the vibrational properties of the phases. These calculations are mostly performed in the harmonic approximation, using empirical or ab-initio force fields. In the case of aperiodic and dynamic systems such as liquids or solutions, similar calculations can be done using finite-size molecular clusters or snapshots obtained from molecular dynamics (MD) runs. It is however difficult to assess the effect of these approximate models on the isotopic fractionation properties. In this work we present a systematic study of the calculation of the D/H and 18O/16O equilibrium fractionation factors in water for the liquid/vapour and ice/vapour phases using several levels of theory within the simulations. Namely, we use a thermodynamic integration approach based on Path Integral MD calculations (PIMD) and an empirical potential model of water. Compared with standard MD, PIMD takes into account quantum effects in the thermodynamic modeling of systems and the exact fractionation factor for a given potential can be obtained. We compare these exact results with those of modeling strategies usually used, which involve the mapping of the quantum system on its harmonic counterpart. The results show the importance of including configurational disorder for the estimation of isotope fractionation in liquid phases. In addition, the convergence of the fractionation factor as a function of parameters such as the size of the simulated system and multiple isotope substitution is analyzed, showing that isotope fractionation is essentially a local effect in
Ronacher, B; Westwig, E; Wehner, R
2006-09-01
When performing foraging trips desert ants of the genus Cataglyphis continuously process and update a ;home vector' that enables them to return to their nest on the shortest route. This capacity of path integration requires two types of information: (i) information about the travelling directions, and (ii) odometric information about the distances travelled in a particular direction. We have investigated how these two necessary pieces of information interact within the path integration processor. The specific question is: how do the ants process distance information if there is no simultaneous input from the sky compass available. Ants were trained to forage in a ;Z'-shaped channel system, the three segments of which joined at right angles. Individual animals were transferred from the feeder to a test field where their homing paths could be observed. In the crucial tests the middle segment of the maze was covered by orange Perspex that did not transmit the UV part of the spectrum, and thus precluded the perception of polarization patterns. Changes of the ant's processing of odometric information within this channel segment directly translate into a change in homing direction on the test field. The results indicate that the odometric information about travelling distance is largely ignored for path integration if there is no simultaneous input from the sky-view-based compass. They further show that idiothetic information cannot adequately substitute for the polarization compass to infer travelling directions.
Barnett-Cowan, Michael; Meilinger, Tobias; Vidal, Manuel; Teufel, Harald; Bülthoff, Heinrich H
2012-05-10
Path integration is a process in which self-motion is integrated over time to obtain an estimate of one's current position relative to a starting point (1). Humans can do path integration based exclusively on visual (2-3), auditory (4), or inertial cues (5). However, with multiple cues present, inertial cues - particularly kinaesthetic - seem to dominate (6-7). In the absence of vision, humans tend to overestimate short distances (<5 m) and turning angles (<30°), but underestimate longer ones (5). Movement through physical space therefore does not seem to be accurately represented by the brain. Extensive work has been done on evaluating path integration in the horizontal plane, but little is known about vertical movement (see (3) for virtual movement from vision alone). One reason for this is that traditional motion simulators have a small range of motion restricted mainly to the horizontal plane. Here we take advantage of a motion simulator (8-9) with a large range of motion to assess whether path integration is similar between horizontal and vertical planes. The relative contributions of inertial and visual cues for path navigation were also assessed. 16 observers sat upright in a seat mounted to the flange of a modified KUKA anthropomorphic robot arm. Sensory information was manipulated by providing visual (optic flow, limited lifetime star field), vestibular-kinaesthetic (passive self motion with eyes closed), or visual and vestibular-kinaesthetic motion cues. Movement trajectories in the horizontal, sagittal and frontal planes consisted of two segment lengths (1st: 0.4 m, 2nd: 1 m; ±0.24 m/s(2) peak acceleration). The angle of the two segments was either 45° or 90°. Observers pointed back to their origin by moving an arrow that was superimposed on an avatar presented on the screen. Observers were more likely to underestimate angle size for movement in the horizontal plane compared to the vertical planes. In the frontal plane observers were more likely to
Hayes, Robin L; Paddison, Stephen J; Tuckerman, Mark E
2009-12-31
The mono-, di-, and tetrahydrates of trifluoromethanesulfonic acid, which contain characteristic H(3)O(+), H(5)O(2)(+), and H(9)O(4)(+) structures, provide model systems for understanding proton transport in materials with high perfluorosulfonic acid density such as perfluorosulfonic acid membranes commonly employed in hydrogen fuel cells. Ab initio molecular dynamics simulations indicate that protons in these solids are predisposed to transfer to the water most strongly bound to sulfonate groups via a Grotthuss-type mechanism, but quickly return to the most solvated defect structure either due to the lack of a nearby species to stabilize the new defect or a preference for the proton to be maximally hydrated. Path integral molecular dynamics of the mono- and dihydrate reveal significant quantum effects that facilitate proton transfer to the "presolvated" water or SO(3)(-) in the first solvation shell and increase the Zundel character of all the defects. These trends are quantified in free energy profiles for each bonding environment. Hydrogen bonding criteria for HOH-OH(2) and HOH-O(3)S are extracted from the two-dimensional potential of mean force. The quantum radial distribution function, radius of gyration, and root-mean-square displacement position correlation function show that the protonic charge is distributed over two or more water molecules. Metastable structural defects with one excess proton shared between two sulfonate groups and another Zundel or Eigen type cation defect are found for the mono- and dihydrate but not for the tetrahydrate crystal. Results for the tetrahydrate native crystal exhibit minor differences at 210 and 250 K. IR spectra are calculated for all native and stable defect structures. Graph theory techniques are used to characterize the chain lengths and ring sizes in the hydrogen bond network. Low conductivities when limited water is present may be attributable to trapping of protons between SO(3)(-) groups and the increased
Different strategies for spatial updating in yaw and pitch path integration.
Goeke, Caspar M; König, Peter; Gramann, Klaus
2013-01-01
Research in spatial navigation revealed the existence of discrete strategies defined by the use of distinct reference frames during virtual path integration. The present study investigated the distribution of these navigation strategies as a function of gender, video gaming experience, and self-estimates of spatial navigation abilities in a population of 300 subjects. Participants watched videos of virtual passages through a star-field with one turn in either the horizontal (yaw) or the vertical (pitch) axis. At the end of a passage they selected one out of four homing arrows to indicate the initial starting location. To solve the task, participants could employ two discrete strategies, navigating within either an egocentric or an allocentric reference frame. The majority of valid subjects (232/260) consistently used the same strategy in more than 75% of all trials. With that approach 33.1% of all participants were classified as Turners (using an egocentric reference frame on both axes) and 46.5% as Non-turners (using an allocentric reference frame on both axes). 9.2% of all participants consistently used an egocentric reference frame in the yaw plane but an allocentric reference frame in the pitch plane (Switcher). Investigating the influence of gender on navigation strategies revealed that females predominantly used the Non-turner strategy while males used both the Turner and the Non-turner strategy with comparable probabilities. Other than expected, video gaming experience did not influence strategy use. Based on a strong quantitative basis with the sample size about an order of magnitude larger than in typical psychophysical studies these results demonstrate that most people reliably use one out of three possible navigation strategies (Turners, Non-turners, Switchers) for spatial updating and provides a sound estimate of how those strategies are distributed within the general population.
NASA Astrophysics Data System (ADS)
Koda, Shin-Ichi; Takatsuka, Kazuo
2011-03-01
The coherent path integral is generalized such that the identity operator represented in a complete (actually overcomplete) set of the coherent states with the “time-variable” exponents are inserted between two consecutive short-time propagators. Since such a complete set of any given exponent can constitute the identity operator, the exponent may be varied from time to time without loss of generality as long as it is set common to all the Gaussians. However, a finite truncation of the coherent state expansion should result in different values of the propagator depending on the choice of the exponents. Furthermore, approximation methodology to treat with the exact propagator can also depend on this choice, and thereby many different semiclassical propagators may emerge from these combinations. Indeed, we show that the well-known semiclassical propagators such as those of Van Vleck, Herman-Kluk, Heller’s thawed Gaussian, and many others can be derived in a systematic manner, which enables one to comprehend these semiclassical propagators from a unified point of view. We are particularly interested in our generalized form of the Herman-Kluk propagator, since the relative accuracy of this propagator has been well established by Kay, and since, nevertheless, its derivation was not necessarily clear. Thus our generalized Herman-Kluk propagator replaces the classical Hamiltonian with a Gaussian averaged quantum Hamiltonian, generating non-Newtonian trajectories. We perform a numerical test to assess the quality of such a family of generalized Herman-Kluk propagators and find that the original Herman-Kluk gives an accurate result. The reason why this has come about is also discussed.
NASA Astrophysics Data System (ADS)
Ishii, S.; Koyama, M.; Baron, P.; Iwai, H.; Mizutani, K.; Itabe, T.; Sato, A.; Asai, K.
2013-05-01
The National Institute of Information and Communications Technology (NICT) has made a great deal of effort to develop a coherent 2 μm differential absorption and wind lidar (Co2DiaWiL) for measuring CO2 and wind speed. First, coherent Integrated Path Differential Absorption (IPDA) lidar experiments were conducted using the Co2DiaWiL and a foothill target (tree and ground surface) located about 7.12 km south of NICT on 11, 27, and 28 December 2010. The detection sensitivity of a 2 μm IPDA lidar was examined in detail using the CO2 concentration measured by the foothill reflection. The precisions of CO2 measurements for the foothill target and 900, 4500 and 27 000 shot pairs were 6.5, 2.8, and 1.2%, respectively. The results indicated that a coherent IPDA lidar with a laser operating at a high pulse repetition frequency of a few tens of KHz is necessary for XCO2 (column-averaged dry air mixing ratio of CO2) measurement with a precision of 1-2 ppm in order to observe temporal and spatial variations in the CO2. Statistical comparisons indicated that, although a small amount of in situ data and the fact that they were not co-located with the foothill target made comparison difficult, the CO2 volume mixing ratio obtained by the Co2DiaWiL measurements for the foothill target and atmospheric returns was about -5 ppm lower than the 5 min running averages of the in situ sensor. Not only actual difference of sensing volume or the natural variability of CO2 but also the fluctuations of temperature could cause this difference. The statistical results indicated that there were no biases between the foothill target and atmospheric return measurements. The 2 μm coherent IPDA lidar can detect the CO2 volume mixing ratio change of 3% in the 5 min signal integration. In order to detect the position of the foothill target, to measure a range with a high SNR (signal-to-noise ratio), and to reduce uncertainty due to the presence of aerosols and clouds, it is important to make a
Lagin, L J; Bettenhauasen, R C; Bowers, G A; Carey, R W; Edwards, O D; Estes, C M; Demaret, R D; Ferguson, S W; . Fisher, J M; Ho, J C; Ludwigsen, A P; Mathisen, D G; Marshall, C D; Matone, J M; McGuigan, D L; Sanchez, R J; Shelton, R T; Stout, E A; Tekle, E; Townsend, S L; Van Arsdall, P J; Wilson, E F
2007-09-11
diagnostics, in preparation for project completion in 2009. Additional capabilities to support fusion ignition shots in a National Ignition Campaign (NIC) beginning in 2010 will include a cryogenic target system, target diagnostics, and integrated experimental shot data analysis with tools for data visualization and archiving. This talk discusses the current status of the control system implementation and discusses the plan to complete the control system on the path to ignition.
Durlak, Piotr; Morrison, Carole A; Middlemiss, Derek S; Latajka, Zdzislaw
2007-08-14
We have studied the double proton transfer (DPT) reaction in the cyclic dimer of chloroacetic acid using both classical and path integral Car-Parrinello molecular dynamics. We also attempt to quantify the errors in the potential energy surface that arise from the use of a pure density functional. In the classical dynamics a clear reaction mechanism can be identified, where asynchronized DPT arises due to coupling between the O-H stretching oscillator and several low energy intermolecular vibrational modes. This mechanism is considerably altered when quantum tunneling is permitted in the simulation. The introduction of path integrals leads to considerable changes in the thermally averaged molecular geometry, leading to shorter and more centered hydrogen bond linkages.
NASA Astrophysics Data System (ADS)
Durlak, Piotr; Morrison, Carole A.; Middlemiss, Derek S.; Latajka, Zdzislaw
2007-08-01
We have studied the double proton transfer (DPT) reaction in the cyclic dimer of chloroacetic acid using both classical and path integral Car-Parrinello molecular dynamics. We also attempt to quantify the errors in the potential energy surface that arise from the use of a pure density functional. In the classical dynamics a clear reaction mechanism can be identified, where asynchronized DPT arises due to coupling between the O-H stretching oscillator and several low energy intermolecular vibrational modes. This mechanism is considerably altered when quantum tunneling is permitted in the simulation. The introduction of path integrals leads to considerable changes in the thermally averaged molecular geometry, leading to shorter and more centered hydrogen bond linkages.
Exact solution of the Feynman-Kac path integral for a point potential in an infinite square well
NASA Astrophysics Data System (ADS)
Rejcek, James M.; Fazleev, Nail G.; Fry, John L.
2004-10-01
The solution of the Feynman-Kac path integral for a point potential in an infinite square well can be understood in terms of symmetric and anti-symmetric eigenstates of the Hamiltonian. If one is not careful in the use of the boundary conditions, it would appear that the even reflection states are not allowed as the solutions. Numerical simulation results for the Feynman-Kac path integral are compared with the analytical solutions. It is also shown that as the magnitude of the point potential is increased the energy spectrum shifts to higher values, and the energy eigenvalues approach the solutions obtained for an infinite well half the size of the original. This effect has implications on the entropy problem known as Maxwell's Demon.
Ab initio path integral molecular dynamics simulation study on the dihydrogen bond of NH4+⋯BeH2
NASA Astrophysics Data System (ADS)
Hayashi, Aiko; Shiga, Motoyuki; Tachikawa, Masanori
2005-07-01
An ab initio path integral molecular dynamics simulation has been performed to study the quantum and thermal effects of a dihydrogen bonded cation, NH4+⋯BeH2. In this system, an attractive interaction exists between two neighboring hydrogen atoms as N δ- H δ+ ⋯H δ- Be δ+ involving large-amplitude of vibration. Some properties playing a key role for this dihydrogen bonded system, such as the bond length, bond angle, and distribution of atomic charges, are investigated in detail by comparing the results of path integral and classical molecular dynamics with those of the equilibrium structure. It was found that the atomic charges of H δ+ and H δ- are decreased and the dihydrogen H δ+ ⋯H δ- bond length is expanded as the thermal and zero-point quantum effects.
NASA Astrophysics Data System (ADS)
Kamibayashi, Yuki; Miura, Shinichi
2016-08-01
In the present study, variational path integral molecular dynamics and associated hybrid Monte Carlo (HMC) methods have been developed on the basis of a fourth order approximation of a density operator. To reveal various parameter dependence of physical quantities, we analytically solve one dimensional harmonic oscillators by the variational path integral; as a byproduct, we obtain the analytical expression of the discretized density matrix using the fourth order approximation for the oscillators. Then, we apply our methods to realistic systems like a water molecule and a para-hydrogen cluster. In the HMC, we adopt two level description to avoid the time consuming Hessian evaluation. For the systems examined in this paper, the HMC method is found to be about three times more efficient than the molecular dynamics method if appropriate HMC parameters are adopted; the advantage of the HMC method is suggested to be more evident for systems described by many body interaction.
On Dirac-Coulomb problem in (2+1) dimensional space-time and path integral quantization
Haouat, S.; Chetouani, L.
2012-06-15
The problem of Dirac particle interacting with Coulomb potential in (2+1) dimensions is formulated in the framework of super-symmetric path integrals where the spin degrees of freedom are described by odd Grassmannian variables. The relative propagator is expressed through Cartesian coordinates in a Hamiltonian form by the use of an adequate transformation. The passage to the polar coordinates permitted us to calculate the fixed energy Green's function and to extract bound states and associating wave functions.
NASA Astrophysics Data System (ADS)
Ingber, Lester; Nunez, Paul L.
1995-05-01
We present high-resolution path-integral calculations of a previously developed model of short-term memory in neocortex. These calculations, made possible with supercomputer resources, supplant similar calculations made by Ingber [Phys. Rev. E 49, 4652 (1994)] and support coarser estimates made by Ingber [Phys. Rev. A 29, 3346 (1984)]. We also present a current experimental context for the relevance of these calculations using the approach of statistical mechanics of neocortical interactions, especially in the context of electroencephalographic data.
NASA Astrophysics Data System (ADS)
Wagner, Gerd; Maxwell, Stephen; Plusquellic, David
2016-06-01
Integrated path concentrations of ambient levels of carbon dioxide and methane have been measured during nighttime periods at NIST, Boulder (CO, USA), using a ground-based, eyesafe laser system. In this contribution, we describe the transmitter and receiver system, demonstrate measurements of CO2 and CH4 in comparison with an in situ point sensor measurement using a commercial cavity ring-down instrument, and demonstrate a speckle noise reduction method.
NASA Astrophysics Data System (ADS)
Fix, Andreas; Quatrevalet, Mathieu; Witschas, Benjamin; Wirth, Martin; Büdenbender, Christian; Amediek, Axel; Ehret, Gerhard
2016-06-01
The stringent requirements for both the frequency stability and power reference represent a challenging task for Integrated Path Differential Absorption Lidars (IPDA) to measure greenhouse gas columns from satellite or aircraft. Currently, the German-French methane mission MERLIN (Methan Remote Lidar Mission) is prepared. At the same time CHARM-F, an aircraft installed system has been developed at DLR as an airborne demonstrator for a spaceborne greenhouse gas mission. The concepts and realization of these important sub-systems are discussed.
NASA Astrophysics Data System (ADS)
Bock, Wolfgang; Capraro, Patrick
2017-02-01
We identify the integrand for the Hamiltonian path integral in space representation as a Kondratiev distribution. For this purpose we use methods from white noise analysis to compute also the Green's function of the underlying Schrödinger equation. We show that its generalized expectation solves the Schrödinger equation and that a functional form of the canonical commutation realtions is fulfilled.
NASA Astrophysics Data System (ADS)
Predescu, Cristian
2004-05-01
In this paper I provide significant mathematical evidence in support of the existence of direct short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and bounded from below potentials. While for Theorem 2, which is “experimental,” I only provide a “physicist’s” proof, I believe the present development is mathematically sound. As a verification, I explicitly construct two short-time approximations to the density matrix having convergence orders 3 and 4, respectively. Furthermore, in Appendix B, I derive the convergence constant for the trapezoidal Trotter path integral technique. The convergence orders and constants are then verified by numerical simulations. While the two short-time approximations constructed are of sure interest to physicists and chemists involved in Monte Carlo path integral simulations, the present paper is also aimed at the mathematical community, who might find the results interesting and worth exploring. I conclude the paper by discussing the implications of the present findings with respect to the solvability of the dynamical sign problem appearing in real-time Feynman path integral simulations.
Hironaka, Mantaro; Tojo, Sumio; Nomakuchi, Shintaro; Filippi, Lisa; Hariyama, Takahiko
2007-06-01
Females of the subsocial shield bug, Parastrachia japonensis (Parastrachiidae), are central-place foragers, collecting drupes for their young from nearby host trees by walking along the forest floor both during the day and at night. Because burrows are often some distance from the drupe-shedding tree, the bugs must repeatedly leave their burrows, search for drupes, and return to the burrows. After a bug leaves its burrow, it searches arduously until it encounters a drupe. When a drupe is obtained, the bug always takes the shortest route back to its burrow. It has been clarified that this bug utilizes path integration during diurnal provisioning excursions. In this paper, we examined nocturnal behavior and some parameters of the path integration utilized by P. japonensis. There were no observable differences between day and night in the patterns of foraging and direct-homing behavior. When the bug was displaced to another position during the day or night, it always walked straight toward the fictive burrow, the site where the burrow should be if it had been displaced along with the bug, and then displayed searching behavior in the vicinity of the fictive burrow. The distance of the straight run corresponded accurately with a straight line between the burrow and the place where the bug obtained the drupe. These results indicate that P. japonensis orients toward the burrow using path integration both during diurnal and nocturnal provisioning behavior.
Agarwal, Animesh Delle Site, Luigi
2015-09-07
Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however, computationally this technique is very demanding. The above mentioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One of the possible solutions to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this paper, we show the simulation of liquid water at room conditions where AdResS, in its latest and more accurate Grand-Canonical-like version (GC-AdResS), is merged with two of the most relevant PIMD techniques available in the literature. The comparison of our results with those reported in the literature and/or with those obtained from full PIMD simulations shows a highly satisfactory agreement.
Schmidt, Matthew; Constable, Steve; Ing, Christopher; Roy, Pierre-Nicholas
2014-06-21
We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψ{sub T}, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 − 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.
NASA Astrophysics Data System (ADS)
Agarwal, Animesh; Delle Site, Luigi
2015-09-01
Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however, computationally this technique is very demanding. The above mentioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One of the possible solutions to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this paper, we show the simulation of liquid water at room conditions where AdResS, in its latest and more accurate Grand-Canonical-like version (GC-AdResS), is merged with two of the most relevant PIMD techniques available in the literature. The comparison of our results with those reported in the literature and/or with those obtained from full PIMD simulations shows a highly satisfactory agreement.
Hayes, Robin L; Paddison, Stephen J; Tuckerman, Mark E
2011-06-16
Trifluoromethanesulfonic acid hydrates provide a well-defined system to study proton dissociation and transport in perfluorosulfonic acid membranes, typically used as the electrolyte in hydrogen fuel cells, in the limit of minimal water. The triflic acid pentahydrate crystal (CF(3)SO(3)H·5H(2)O) is sufficiently aqueous that it contains an extended three-dimensional water network. Despite it being extended, however, long-range proton transport along the network is structurally unfavorable and would require considerable rearrangement. Nevertheless, the triflic acid pentahydrate crystal system can provide a clear picture of the preferred locations of local protonic defects in the water network, which provides insights about related structures in the disordered, low-hydration environment of perfluorosulfonic acid membranes. Ab initio molecular dynamics simulations reveal that the proton defect is most likely to transfer to the closest water that has the expected presolvation and only contains water in its first solvation shell. Unlike the tetrahydrate of triflic acid (CF(3)SO(3)H·4H(2)O), there is no evidence of the proton preferentially transferring to a water molecule bridging two of the sulfonate groups. However, this could be an artifact of the crystal structure since the only such water molecule is separated from the proton by long O-O distances. Hydrogen bonding criteria, using the two-dimensional potential of mean force, are extracted. Radial distribution functions, free energy profiles, radii of gyration, and the root-mean-square displacement computed from ab initio path integral molecular dynamics simulations reveal that quantum effects do significantly extend the size of the protonic defect and increase the frequency of proton transfer events by nearly 15%. The calculated IR spectra confirm that the dominant protonic defect mostly exists as an Eigen cation but contains some Zundel ion characteristics. Chain lengths and ring sizes determined from the
Montoya-Castillo, Andrés; Reichman, David R
2017-01-14
We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In addition, the expressions derived here provide an exact and facile interface with quasi- and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function Czz(t)=Re⟨σz(0)σz(t)⟩ for the spin-boson model with systematic convergence to the exact sampling function. Importantly, the numerically exact nature of the scheme presented here and its compatibility with semiclassical methods allows for the systematic testing of commonly used approximations for the Wigner-transformed canonical density.
NASA Astrophysics Data System (ADS)
Montoya-Castillo, Andrés; Reichman, David R.
2017-01-01
We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In addition, the expressions derived here provide an exact and facile interface with quasi- and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function Cz z(t ) =Re ⟨σz(0 ) σz(t ) ⟩ for the spin-boson model with systematic convergence to the exact sampling function. Importantly, the numerically exact nature of the scheme presented here and its compatibility with semiclassical methods allows for the systematic testing of commonly used approximations for the Wigner-transformed canonical density.
Shek, Daniel T. L.
2012-01-01
An integration of the qualitative evaluation findings collected from program implementers conducting the Project P.A.T.H.S. (Positive Adolescent Training through Holistic Social Programmes) in different years (n = 177 participants in 36 focus groups) was carried out. General qualitative data analyses utilizing intra and interrater reliability techniques were performed. Results showed that the descriptors used to describe the program and the metaphors named by the informants that could stand for the program were generally positive in nature. Program participants also perceived the program to be beneficial to the development of the students in different psychosocial domains. The present study further supports the effectiveness of the Tier 1 Program of the Project P.A.T.H.S. in Hong Kong based on the perspective of the program implementers. PMID:22666139
Path dependence of J in three numerical examples. [J integral in three crack propagation problems
NASA Technical Reports Server (NTRS)
Karabin, M. E., Jr.; Swedlow, J. L.
1979-01-01
Three cracked geometries are studied with the aid of a new finite element model. The procedure employs a variable singularity at the crack tip that tracks changes in the material response during the loading process. Two of the problems are tension-loaded center-crack panels and the other is a three-point bend specimen. Results usually agree with other numerical and analytical analyses, except the finding that J is path dependent as a substantial plastic zone develops. Credible J values are obtained near the crack tip and J shows a significant increase as the radius of J path increases over two orders of magnitude. Incremental and deformation theories are identical provided the stresses exhibit proportionality found in the far field stresses but not near the tip.
Vulnerabilities, Influences and Interaction Paths: Failure Data for Integrated System Risk Analysis
NASA Technical Reports Server (NTRS)
Malin, Jane T.; Fleming, Land
2006-01-01
We describe graph-based analysis methods for identifying and analyzing cross-subsystem interaction risks from subsystem connectivity information. By discovering external and remote influences that would be otherwise unexpected, these methods can support better communication among subsystem designers at points of potential conflict and to support design of more dependable and diagnosable systems. These methods identify hazard causes that can impact vulnerable functions or entities if propagated across interaction paths from the hazard source to the vulnerable target. The analysis can also assess combined impacts of And-Or trees of disabling influences. The analysis can use ratings of hazards and vulnerabilities to calculate cumulative measures of the severity and importance. Identification of cross-subsystem hazard-vulnerability pairs and propagation paths across subsystems will increase coverage of hazard and risk analysis and can indicate risk control and protection strategies.
A comparison of NH{sub 3} point monitoring and diode laser based path integrated measurements
Goldstein, N.; Richtsmeier, S.C.; Lee, J.; Bien, F.; Fetzer, G.J.; Groff, K.W.
1994-12-31
Measurements made using two different types of ammonia monitors during a two-month field study in the summer of 1994 are discussed. The first was a diode-laser based open path monitor designed for automated operation in an industrial environment. The second is a monitoring analyzer based on thermal decomposition of ammonia to NO and subsequent analysis by O{sub 3}-NO chemiluminescence. The two monitors provided consistent measurements of ammonia concentration during weeks of continuous unattended operation.
NASA Astrophysics Data System (ADS)
Lemmens, D.; Wouters, M.; Tempere, J.; Foulon, S.
2008-07-01
We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is demonstrated by extending the realm of closed-form option price formulas to the case where both the volatility and interest rates are stochastic. This flexibility is promising for the treatment of exotic options. Our analytical formulas are tested with numerical Monte Carlo simulations.
NASA Astrophysics Data System (ADS)
Saito, Hiroki
2016-05-01
Motivated by recent experiments [H. Kadau et al., http://doi.org/10.1038/nature16485, Nature (London) 530, 194 (2016); I. Ferrier-Barbut et al., http://arxiv.org/abs/1601.03318, arXiv:1601.03318] and theoretical prediction (F. Wächtler and L. Santos, http://arxiv.org/abs/1601.04501, arXiv:1601.04501), the ground state of a dysprosium Bose-Einstein condensate with strong dipole-dipole interaction is studied by the path-integral Monte Carlo method. It is shown that quantum fluctuation can stabilize the condensate against dipolar collapse.
NASA Astrophysics Data System (ADS)
Kawashima, Yukio; Tachikawa, Masanori
2013-05-01
Ab initio path integral molecular dynamics simulation was performed to understand the nuclear quantum effect on the hydrogen bond of hydrogen malonate anion. Static calculation predicted the proton transfer barrier as 0.12 kcal/mol. Conventional ab initio molecular dynamics simulation at 300 K found proton distribution with a double peak on the proton transfer coordinate. Inclusion of thermal effect alone elongates the hydrogen bond length, which increases the barrier height. Inclusion of nuclear quantum effect washes out this barrier, and distributes a single broad peak in the center. H/D isotope effect on the proton transfer is also discussed.
Ab initio path integral simulation study on 16O/ 18O isotope effect in water and hydronium ion
NASA Astrophysics Data System (ADS)
Tachikawa, Masanori; Shiga, Motoyuki
2005-05-01
An ab initio path integral molecular dynamics simulation has been performed to study the 16O and 18O isotopomers for a water molecule and a hydronium ion at temperature 300 K. The average O-H bond length of H 218O molecule is slightly shorter than that of H 216O molecule, while that of H 318O + is slightly longer than that of H 316O +. For hydronium ions, the Walden inversion of H 318O +, as well as D 316O +, is found to be more restrained than that of H 316O +. The isotope effect in the electronic structure and thermochemical properties for these isotopomers are also shown.
NASA Astrophysics Data System (ADS)
Yoshikawa, Takehiro; Sugawara, Shuichi; Takayanagi, Toshiyuki; Shiga, Motoyuki; Tachikawa, Masanori
2010-08-01
Full-dimensional path-integral molecular dynamics simulations were performed to determine whether the double proton transfer tautomerization of porphycene is a concerted or a stepwise process. We employed an on-the-fly direct dynamics technique at the semiempirical PM6 method whose parameters were determined so as that the relative energies of the stationary points approximately reproduce previously reported electronic structure calculations. It was found that double proton transfer occurs dominantly through the concerted pathway via the second-order saddle point structure and that contribution of the stepwise mechanism increases with a temperature increase. Nuclear quantum effects play essential roles in determining the proton transfer mechanism.
NASA Astrophysics Data System (ADS)
Kakizaki, Akira; Takayanagi, Toshiyuki; Shiga, Motoyuki
2007-11-01
Path integral molecular dynamics simulations for the H6+ and D6+ cluster cations have been carried out in order to understand the floppy nature of their molecular structure due to quantum-mechanical fluctuation. A full-dimensional analytical potential energy surface for the ground electronic state of H6+ has been developed on the basis of accurate ab initio electronic structure calculations at the CCSD(T)/cc-pVTZ level. It is found that the outer H 2(D 2) nuclei rotate almost freely and that the probability density distributions of the central H 2(D 2) nuclei show strong spatial delocalization.
NASA Astrophysics Data System (ADS)
Müser, Martin H.
2001-04-01
Classical and path integral molecular dynamics (PIMD) simulations are used to study α and β quartz in a large range of temperatures at zero external stress. PIMD account for quantum fluctuations of atomic vibrations, which can modify material properties at temperatures below the Debye temperature. The difference between classical and quantum mechanical results for bond lengths, bond angles, elastic moduli, and some dynamical properties is calculated and comparison to experimental data is done. Only quantum mechanical simulations are able to reproduce the correct thermomechanical properties below room temperature. It is discussed in how far classical and PIMD simulations can be helpful in constructing improved potential energy surfaces for silica.
NASA Astrophysics Data System (ADS)
Miura, Shinichi; Okazaki, Susumu
2001-09-01
In this paper, the path integral molecular dynamics (PIMD) method has been extended to employ an efficient approximation of the path action referred to as the pair density matrix approximation. Configurations of the isomorphic classical systems were dynamically sampled by introducing fictitious momenta as in the PIMD based on the standard primitive approximation. The indistinguishability of the particles was handled by a pseudopotential of particle permutation that is an extension of our previous one [J. Chem. Phys. 112, 10 116 (2000)]. As a test of our methodology for Boltzmann statistics, calculations have been performed for liquid helium-4 at 4 K. We found that the PIMD with the pair density matrix approximation dramatically reduced the computational cost to obtain the structural as well as dynamical (using the centroid molecular dynamics approximation) properties at the same level of accuracy as that with the primitive approximation. With respect to the identical particles, we performed the calculation of a bosonic triatomic cluster. Unlike the primitive approximation, the pseudopotential scheme based on the pair density matrix approximation described well the bosonic correlation among the interacting atoms. Convergence with a small number of discretization of the path achieved by this approximation enables us to construct a method of avoiding the problem of the vanishing pseudopotential encountered in the calculations by the primitive approximation.
NASA Astrophysics Data System (ADS)
Steill, J. D.; Compton, R. N.; Hager, J. S.
2006-12-01
Ground-based solar infrared absorption spectroscopy coupled with open-path spectroscopy provides a means for analysis of the highly variable contribution of the boundary layer to problems of radiative transfer and atmospheric chemistry. This is of particular importance in geographic regions of significant local anthropogenic influence and large tropospheric fluctuations in general. A Bomem DA8 FT-IR integrated with a sun-tracking and open-path system (~0.5 km) is located at The University of Tennessee, in downtown Knoxville and near The Great Smoky Mountains National Park, an area known for problematic air quality. From atmospheric absorption spectra, boundary layer concentrations as well as total column abundances and vertical concentration profiles are derived. A record of more than 1000 solar-sourced atmospheric spectra covering a period greater than three years in duration is under analysis to characterize the limit of precision in total column abundance determinations for many gases such as O3, CO, CH4, N2O, HF and CO2. Initial efforts using atmospheric O2 as a calibration indicate the solar-sourced spectra may not meet the precision required for the highly accurate atmospheric CO2 quantification by such global efforts as the OCO and NDSC. However, the determined variability of CO2 and other gas concentrations is statistically significant and is indicative of local concentration fluxes pertinent to the regional atmospheric chemistry. This is therefore an important data record in the southeastern United States, a somewhat under- sampled geographic region. In addition to providing a means to improve the analysis of solar spectra, the open-path data is useful for elucidation of seasonal and diurnal trends in the trace gas concentrations. This provides an urban air quality monitor in addition to improving the description of the total atmospheric composition, as the open-path system is stable and permanent.
NASA Astrophysics Data System (ADS)
Janakiraman, Deepika; Sebastian, K. L.
2012-12-01
Lévy flights can be described using a Fokker-Planck equation, which involves a fractional derivative operator in the position coordinate. Such an operator has its natural expression in the Fourier domain. Starting with this, we show that the solution of the equation can be written as a Hamiltonian path integral. Though this has been realized in the literature, the method has not found applications as the path integral appears difficult to evaluate. We show that a method in which one integrates over the position coordinates first, after which integration is performed over the momentum coordinates, can be used to evaluate several path integrals that are of interest. Using this, we evaluate the propagators for (a) free particle, (b) particle subjected to a linear potential, and (c) harmonic potential. In all the three cases, we have obtained results for both overdamped and underdamped cases.
Wendland, D.; Ballenegger, V.; Alastuey, A.
2014-11-14
We compute two- and three-body cluster functions that describe contributions of composite entities, like hydrogen atoms, ions H{sup −}, H{sub 2}{sup +}, and helium atoms, and also charge-charge and atom-charge interactions, to the equation of state of a hydrogen-helium mixture at low density. A cluster function has the structure of a truncated virial coefficient and behaves, at low temperatures, like a usual partition function for the composite entity. Our path integral Monte Carlo calculations use importance sampling to sample efficiently the cluster partition functions even at low temperatures where bound state contributions dominate. We also employ a new and efficient adaptive discretization scheme that allows one not only to eliminate Coulomb divergencies in discretized path integrals, but also to direct the computational effort where particles are close and thus strongly interacting. The numerical results for the two-body function agree with the analytically known quantum second virial coefficient. The three-body cluster functions are compared at low temperatures with familiar partition functions for composite entities.
NASA Astrophysics Data System (ADS)
Wendland, D.; Ballenegger, V.; Alastuey, A.
2014-11-01
We compute two- and three-body cluster functions that describe contributions of composite entities, like hydrogen atoms, ions H-, H_2^+, and helium atoms, and also charge-charge and atom-charge interactions, to the equation of state of a hydrogen-helium mixture at low density. A cluster function has the structure of a truncated virial coefficient and behaves, at low temperatures, like a usual partition function for the composite entity. Our path integral Monte Carlo calculations use importance sampling to sample efficiently the cluster partition functions even at low temperatures where bound state contributions dominate. We also employ a new and efficient adaptive discretization scheme that allows one not only to eliminate Coulomb divergencies in discretized path integrals, but also to direct the computational effort where particles are close and thus strongly interacting. The numerical results for the two-body function agree with the analytically known quantum second virial coefficient. The three-body cluster functions are compared at low temperatures with familiar partition functions for composite entities.
NASA Technical Reports Server (NTRS)
Bernstein, D. R.; Dashen, R.; Flatte, S. M.
1983-01-01
A theory is developed which describes intensity moments for wave propagation through random media. It is shown using the path integral technique that these moments are significantly different from those of a Rayleigh distribution in certain asymptotic regions. The path integral approach is extended to inhomogeneous, anisotropic media possessing a strong deterministic velocity profile. The behavior of the corrections to Rayleigh statistics is examined, and it is shown that the important characteristics can be attributed to a local micropath focusing function. The correction factor gamma is a micropath focusing parameter defined in terms of medium fluctuations. The value of gamma is calculated for three ocean acoustic experiments, using internal waves as the medium fluctuations. It is found that all three experiments show excellent agreement as to the relative values of the intensity moments. The full curved ray is found to yield results that are significantly different from the straight-line approximations. It is noted that these methods are applicable to a variety of experimental situations, including atmospheric optics and radio waves through plasmas.
NASA Astrophysics Data System (ADS)
Kapila, Vivek; Deymier, Pierre; Runge, Keith
2012-02-01
Warm dense matter (WDM) can be characterized by electron temperatures of a few eV and densities an order of magnitude or more beyond ambient. This regime currently lacks any adequate highly developed class of simulation methods. Recent developments in orbital-free Density Functional Theory (ofDFT) aim to provide such a simulation method, however, little benchmark information is available on temperature and pressure dependence of simple but realistic models in WDM regime. The present work aims to fill this critical gap using the restricted path-integral molecular dynamics (rPIMD) method. Within the discrete path integral representation, electrons are described as harmonic necklaces, while, quantum exchange takes the form of cross linking between electron necklaces. The fermion sign problem is addressed by restricting the density matrix to positive values and a molecular dynamics algorithm is employed to sample phase space. Here, we focus on the behavior of strongly correlated electron plasmas under WDM conditions. We compute the kinetic and potential energies and compare them to those obtained with the ofDFT method.
NASA Astrophysics Data System (ADS)
Runge, Keith; Deymier, Pierre
2013-03-01
Recent progress in orbital-free Density Functional Theory (OF-DFT), particularly with regard to temperature dependent functionals, has promise for the simulation of warm dense matter (WDM) systems. WDM includes systems with densities of an order of magnitude beyond ambient or more and temperatures measured in kilokelvin. A challenge for the development of temperature dependent OF-DFT functionals is the lack of benchmark information with temperature and pressure dependence on simple models under WDM conditions. We present an approach to fill this critical gap using the restricted path-integral molecular dynamics (rPIMD) method. Electrons are described as harmonic necklaces within the discrete path integral representation while quantum exchange takes the form of cross linking between electron necklaces. A molecular dynamics algorithm is used to sample phase space and the fermion sign problem is addressed by restricting the density matrix to positive values. The temperature dependence of kinetic energies for the strongly coupled electron plasma is presented for a number of Wigner-Seitz radii in terms of a fourth order Sommerfeld expansion. Supported by US DoE Grant DE-SC0002139
Wong, Kin-Yiu; Xu, Yuqing; York, Darrin M
2014-06-30
Detailed understandings of the reaction mechanisms of RNA catalysis in various environments can have profound importance for many applications, ranging from the design of new biotechnologies to the unraveling of the evolutionary origin of life. An integral step in the nucleolytic RNA catalysis is self-cleavage of RNA strands by 2'-O-transphosphorylation. Key to elucidating a reaction mechanism is determining the molecular structure and bonding characteristics of transition state. A direct and powerful probe of transition state is measuring isotope effects on biochemical reactions, particularly if we can reproduce isotope effect values from quantum calculations. This article significantly extends the scope of our previous joint experimental and theoretical work in examining isotope effects on enzymatic and nonenzymatic 2'-O-transphosphorylation reaction models that mimic reactions catalyzed by RNA enzymes (ribozymes), and protein enzymes such as ribonuclease A (RNase A). Native reactions are studied, as well as reactions with thio substitutions representing chemical modifications often used in experiments to probe mechanism. Here, we report and compare results from eight levels of electronic-structure calculations for constructing the potential energy surfaces in kinetic and equilibrium isotope effects (KIE and EIE) computations, including a "gold-standard" coupled-cluster level of theory [CCSD(T)]. In addition to the widely used Bigeleisen equation for estimating KIE and EIE values, internuclear anharmonicity and quantum tunneling effects were also computed using our recently developed ab initio path-integral method, that is, automated integration-free path-integral method. The results of this work establish an important set of benchmarks that serve to guide calculations of KIE and EIE for RNA catalysis.
Test-Taker Characteristics and Integrated Speaking Test Performance: A Path-Analytic Study
ERIC Educational Resources Information Center
Huang, Heng-Tsung Danny; Hung, Shao-Ting Alan; Hong, He-Ting Vivian
2016-01-01
This study explored the relationships among language proficiency, two selected test-taker characteristics (i.e., topical knowledge and anxiety), and integrated speaking test performance. Data collection capitalized on three sets of instruments: three integrated tasks derived from TOEFL-iBT preparation materials, the state anxiety inventory created…
NASA Astrophysics Data System (ADS)
Filinov, V. S.; Ivanov, Yu. B.; Fortov, V. E.; Bonitz, M.; Levashov, P. R.
2013-03-01
Based on the quasiparticle model of the quark-gluon plasma (QGP), a color quantum path-integral Monte-Carlo (PIMC) method for the calculation of thermodynamic properties and—closely related to the latter—a Wigner dynamics method for calculation of transport properties of the QGP are formulated. The QGP partition function is presented in the form of a color path integral with a new relativistic measure instead of the Gaussian one traditionally used in the Feynman-Wiener path integral. A procedure of sampling color variables according to the SU(3) group Haar measure is developed for integration over the color variable. It is shown that the PIMC method is able to reproduce the lattice QCD equation of state at zero baryon chemical potential at realistic model parameters (i.e., quasiparticle masses and coupling constant) and also yields valuable insight into the internal structure of the QGP. Our results indicate that the QGP reveals quantum liquidlike(rather than gaslike) properties up to the highest considered temperature of 525 MeV. The pair distribution functions clearly reflect the existence of gluon-gluon bound states, i.e., glueballs, at temperatures just above the phase transition, while mesonlike qq¯ bound states are not found. The calculated self-diffusion coefficient agrees well with some estimates of the heavy-quark diffusion constant available from recent lattice data and also with an analysis of heavy-quark quenching in experiments on ultrarelativistic heavy-ion collisions, however, appreciably exceeds other estimates. The lattice and heavy-quark-quenching results on the heavy-quark diffusion are still rather diverse. The obtained results for the shear viscosity are in the range of those deduced from an analysis of the experimental elliptic flow in ultrarelativistic heavy-ions collisions, i.e., in terms the viscosity-to-entropy ratio, 1/4π≲η/S<2.5/4π, in the temperature range from 170 to 440 MeV.
NASA Astrophysics Data System (ADS)
Distasio, Robert A., Jr.; Santra, Biswajit; Ko, Hsin-Yu; Car, Roberto
2014-03-01
In this work, we report highly accurate ab initio path-integral molecular dynamics (AI-PIMD) simulations on liquid water at ambient conditions utilizing the recently developed PBE0+vdW(SC) exchange-correlation functional, which accounts for exact exchange and a self-consistent pairwise treatment of van der Waals (vdW) or dispersion interactions, combined with nuclear quantum effects (via the colored-noise generalized Langevin equation). The importance of each of these effects in the theoretical prediction of the structure of liquid water will be demonstrated by a detailed comparative analysis of the predicted and experimental oxygen-oxygen (O-O), oxygen-hydrogen (O-H), and hydrogen-hydrogen (H-H) radial distribution functions as well as other structural properties. In addition, we will discuss the theoretically obtained proton momentum distribution, computed using the recently developed Feynman path formulation, in light of the experimental deep inelastic neutron scattering (DINS) measurements. DOE: DE-SC0008626, DOE: DE-SC0005180.
The Regional University: Paths of Integration in the Framework of the Bologna Process
ERIC Educational Resources Information Center
Lazarev, G.; Martynenko, O.
2006-01-01
The development of international systems of education is opening the way to accomplish tasks in the sphere of higher education that are common to the world community. The Bologna Process, in the framework of which the educational systems of Europe are becoming integrated, makes it possible for Russia to make a choice of the forms of its…
Simulation of thermal ionization in a dense helium plasma by the Feynman path integral method
NASA Astrophysics Data System (ADS)
Shevkunov, S. V.
2011-04-01
The region of equilibrium states is studied where the quantum nature of the electron component and a strong nonideality of a plasma play a key role. The problem of negative signs in the calculation of equilibrium averages a system of indistinguishable quantum particles with a spin is solved in the macroscopic limit. It is demonstrated that the calculation can be conducted up to a numerical result. The complete set of symmetrized basis wave functions is constructed based on the Young symmetry operators. The combinatorial weight coefficients of the states corresponding to different graphs of connected Feynman paths in multiparticle systems are calculated by the method of random walk over permutation classes. The kinetic energy is calculated using a viral estimator at a finite pressure in a statistical ensemble with flexible boundaries. Based on the methods developed in the paper, the computer simulation is performed for a dense helium plasma in the temperature range from 30000 to 40000 K. The equation of state, internal energy, ionization degree, and structural characteristic of the plasma are calculated in terms of spatial correlation functions. The parameters of a pseudopotential plasma model are estimated.
Dahmen, Hansjürgen; Wahl, Verena L; Pfeffer, Sarah E; Mallot, Hanspeter A; Wittlinger, Matthias
2017-02-15
Air-cushioned spheres are widely used as treadmills to study behavioural and neurophysiological questions in numerous species. We describe an improved spherical treadmill design that reliably registers the path and walking behaviour of an animal walking on top of the sphere. The simple and robust set-up consists of a very light hollowed styrofoam ball supported by an air stream in a hollow half sphere and can be used indoors and outdoors. Two optical mouse sensors provided with lenses of 4.6 mm focal length detect the motion of the sphere with a temporal resolution of more than 200 frames s(-1) and a spatial resolution of less than 0.2 mm. The treadmill can be used in an open- or closed-loop configuration with respect to yaw of the animal. The tethering allows animals to freely adjust their body posture and in the closed-loop configuration to quickly rotate around their yaw axis with their own moment of inertia. In this account, we present the first evidence of naturalistic homing navigation on a spherical treadmill for two species of Cataglyphis desert ants. We were able to evaluate with good precision the walking speed and angular orientation at any time. During homing the ants showed a significant difference in walking speed between the approach and search phases; moreover, they slowed down significantly as soon as they reached zero vector state, the fictive nest position.
The polarization compass dominates over idiothetic cues in path integration of desert ants.
Lebhardt, Fleur; Koch, Julja; Ronacher, Bernhard
2012-02-01
Desert ants, Cataglyphis, use the sky's pattern of polarized light as a compass reference for navigation. However, they do not fully exploit the complexity of this pattern, rather - as proposed previously - they assess their walking direction by means of an approximate solution based on a simplified internal template. Approximate rules are error-prone. We therefore asked whether the ants use additional cues to improve the accuracy of directional decisions, and focused on 'idiothetic' cues, i.e. cues based on information from proprioceptors. We trained ants in a channel system that was covered with a polarization filter, providing only a single e-vector direction as a directional 'celestial' cue. Then we observed their homebound runs on a test field, allowing full view of the sky. In crucial experiments, the ants were exposed to a cue conflict, in which sky compass and idiothetic information disagreed, by training them in a straight channel that provided a change in e-vector direction. The results indicated that the polarization information completely dominates over idiothetic cues. Two path segments with different e-vector orientations are combined linearly to a summed home vector. Our data provide additional evidence that Cataglyphis uses a simplified internal template to derive directional information from the sky's polarization pattern.
NASA Astrophysics Data System (ADS)
Gratton, Steven
2011-09-01
In this paper we present a path integral formulation of stochastic inflation. Volume weighting can be naturally implemented from this new perspective in a very straightforward way when compared to conventional Langevin approaches. With an in-depth study of inflation in a quartic potential, we investigate how the inflaton evolves and how inflation typically ends both with and without volume weighting. The calculation can be carried to times beyond those accessible to conventional Fokker-Planck approaches. Perhaps unexpectedly, complex histories sometimes emerge with volume weighting. The reward for this excursion into the complex plane is an insight into how volume-weighted inflation both loses memory of initial conditions and ends via slow roll. The slow-roll end of inflation mitigates certain “Youngness Paradox”-type criticisms of the volume-weighted paradigm. Thus it is perhaps time to rehabilitate proper-time volume weighting as a viable measure for answering at least some interesting cosmological questions.
Poma, A B; Delle Site, L
2010-06-25
Simulations that couple different molecular models in an adaptive way by changing resolution on the fly allow us to identify the relevant degrees of freedom of a system. This, in turn, leads to a detailed understanding of the essential physics which characterizes a system. While the delicate process of transition from one model to another is well understood for the adaptivity between classical molecular models the same cannot be said for the quantum-classical adaptivity. The main reason for this is the difficulty in describing a continuous transition between two different kinds of physical principles: probabilistic for the quantum and deterministic for the classical. Here we report the basic principles of an algorithm that allows for a continuous and smooth transition by employing the path integral description of atoms.
Knierim, James J; Neunuebel, Joshua P; Deshmukh, Sachin S
2014-02-05
The hippocampus receives its major cortical input from the medial entorhinal cortex (MEC) and the lateral entorhinal cortex (LEC). It is commonly believed that the MEC provides spatial input to the hippocampus, whereas the LEC provides non-spatial input. We review new data which suggest that this simple dichotomy between 'where' versus 'what' needs revision. We propose a refinement of this model, which is more complex than the simple spatial-non-spatial dichotomy. MEC is proposed to be involved in path integration computations based on a global frame of reference, primarily using internally generated, self-motion cues and external input about environmental boundaries and scenes; it provides the hippocampus with a coordinate system that underlies the spatial context of an experience. LEC is proposed to process information about individual items and locations based on a local frame of reference, primarily using external sensory input; it provides the hippocampus with information about the content of an experience.
Özarslan, Evren; Westin, Carl-Fredrik; Mareci, Thomas H.
2016-01-01
The influence of Gaussian diffusion on the magnetic resonance signal is determined by the apparent diffusion coefficient (ADC) and tensor (ADT) of the diffusing fluid as well as the gradient waveform applied to sensitize the signal to diffusion. Estimations of ADC and ADT from diffusion-weighted acquisitions necessitate computations of, respectively, the b-value and b-matrix associated with the employed pulse sequence. We establish the relationship between these quantities and the gradient waveform by expressing the problem as a path integral and explicitly evaluating it. Further, we show that these important quantities can be conveniently computed for any gradient waveform using a simple algorithm that requires a few lines of code. With this representation, our technique complements the multiple correlation function (MCF) method commonly used to compute the effects of restricted diffusion, and provides a consistent and convenient framework for studies that aim to infer the microstructural features of the specimen. PMID:27182208
Zillich, Robert E.
2015-11-15
We construct an accurate imaginary time propagator for path integral Monte Carlo simulations for heterogeneous systems consisting of a mixture of atoms and molecules. We combine the pair density approximation, which is highly accurate but feasible only for the isotropic interactions between atoms, with the Takahashi–Imada approximation for general interactions. We present finite temperature simulations results for energy and structure of molecules–helium clusters X{sup 4}He{sub 20} (X=HCCH and LiH) which show a marked improvement over the Trotter approximation which has a 2nd-order time step bias. We show that the 4th-order corrections of the Takahashi–Imada approximation can also be applied perturbatively to a 2nd-order simulation.
NASA Astrophysics Data System (ADS)
Subramanian, Ramachandran; Schultz, Andrew J.; Kofke, David A.
2017-03-01
We develop an orientation sampling algorithm for rigid diatomic molecules, which allows direct generation of rings of images used for path-integral calculation of nuclear quantum effects. The algorithm treats the diatomic molecule as two independent atoms as opposed to one (quantum) rigid rotor. Configurations are generated according to a solvable approximate distribution that is corrected via the acceptance decision of the Monte Carlo trial. Unlike alternative methods that treat the systems as a quantum rotor, this atom-based approach is better suited for generalization to multi-atomic (more than two atoms) and flexible molecules. We have applied this algorithm in combination with some of the latest ab initio potentials of rigid H2 to compute fully quantum second virial coefficients, for which we observe excellent agreement with both experimental and simulation data from the literature.
NASA Technical Reports Server (NTRS)
Robertson, Franklin R.; Fitzjarrald, Dan E.; Kummerow, Christian D.; Arnold, James E. (Technical Monitor)
2002-01-01
Considerable uncertainty surrounds the issue of whether precipitation over the tropical oceans (30 deg N/S) systematically changes with interannual sea-surface temperature (SST) anomalies that accompany El Nino (warm) and La Nina (cold) events. Time series of rainfall estimates from the Tropical Rainfall Measuring Mission (TRMM Precipitation Radar (PR) over the tropical oceans show marked differences with estimates from two TRMM Microwave Imager (TMI) passive microwave algorithms. We show that path-integrated attenuation derived from the effects of precipitation on the radar return from the ocean surface exhibits interannual variability that agrees closely with the TMI time series. Further analysis of the frequency distribution of PR (2A25 product) rain rates suggests that the algorithm incorporates the attenuation measurement in a very conservative fashion so as to optimize the instantaneous rain rates. Such an optimization appears to come at the expense of monitoring interannual climate variability.
NASA Astrophysics Data System (ADS)
Suzuki, Kimichi; Shiga, Motoyuki; Tachikawa, Masanori
2008-10-01
Path integral molecular dynamics simulation based on the fourth order Trotter expansion has been performed to elucidate the geometrical isotope effect of water dimer anions, H3O2-, D3O2-, and T3O2-, at different temperatures from 50 to 600 K. At low temperatures below 200 K the hydrogen-bonded hydrogen nucleus is near the center of two oxygen atoms with mostly O⋯X⋯O geometry (where X =H, D, or T), while at high temperatures above 400 K, hydrogen becomes more delocalized, showing the coexistence between O⋯X-O and O-X⋯O. The OO distance tends to be shorter as the isotopomer is heavier at low temperatures, while this ordering becomes opposite at high temperatures. It is concluded that the coupling between the OO stretching mode and proton transfer modes is a key to understand such a temperature dependence of a hydrogen-bonded structure.
NASA Astrophysics Data System (ADS)
Shiga, Motoyuki; Takayanagi, Toshiyuki
2003-09-01
The equilibrium structure of the negatively charged water dimer (H 2O) 2- has been studied using the path-integral molecular dynamics simulation. All the atomic motions as well as the excess electron were treated quantum mechanically, employing a semi-empirical model combining a water-water interatomic potential with an electron-water pseudopotential. It is demonstrated that the molecular structure of (H 2O) 2- is more flexible than that of (H 2O) 2; both the donor switching and donor-acceptor interchange can more effectively occur in (H 2O) 2- than in (H 2O) 2. We conclude that this floppy character is a result of the breakdown of the adiabatic Born-Oppenheimer picture.
NASA Astrophysics Data System (ADS)
Torrent, Marc; Geneste, Gregory
2012-02-01
The low-temperature phases of dense hydrogen and deuterium have been investigated using first-principles path-integral molecular dynamics, a technique that we have recently implemented in the ABINIT code and that allows to account for the quantum fluctuations of atomic nuclei. A massively parallelized scheme is applied to produce trajectories of several tens of thousands steps using a 64-atom supercell and a Trotter number of 64. The so-called phases I, II and III are studied and compared to the structures proposed in the literature. The quantum fluctuations produce configurational disorder and are shown to systematically enhance the symmetry of the system: a continuous gain of symmetry in the angular density of probability of the molecules is found from classical particles to quantum D2 and finally to quantum H2. Particular emphasis is made on the ``broken-symmetry'' phase (phase II).
NASA Astrophysics Data System (ADS)
Wong, Kin-Yiu
We have simulated two enzymatic reactions with molecular dynamics (MD) and combined quantum mechanical/molecular mechanical (QM/MM) techniques. One reaction is the hydrolysis of the insecticide paraoxon catalyzed by phosphotriesterase (PTE). PTE is a bioremediation candidate for environments contaminated by toxic nerve gases (e.g., sarin) or pesticides. Based on the potential of mean force (PMF) and the structural changes of the active site during the catalysis, we propose a revised reaction mechanism for PTE. Another reaction is the hydrolysis of the second-messenger cyclic adenosine 3'-5'-monophosphate (cAMP) catalyzed by phosphodiesterase (PDE). Cyclicnucleotide PDE is a vital protein in signal-transduction pathways and thus a popular target for inhibition by drugs (e.g., ViagraRTM). A two-dimensional (2-D) free-energy profile has been generated showing that the catalysis by PDE proceeds in a two-step SN2-type mechanism. Furthermore, to characterize a chemical reaction mechanism in experiment, a direct probe is measuring kinetic isotope effects (KIEs). KIEs primarily arise from internuclear quantum-statistical effects, e.g., quantum tunneling and quantization of vibration. To systematically incorporate the quantum-statistical effects during MD simulations, we have developed an automated integration-free path-integral (AIF-PI) method based on Kleinert's variational perturbation theory for the centroid density of Feynman's path integral. Using this analytic method, we have performed ab initio pathintegral calculations to study the origin of KIEs on several series of proton-transfer reactions from carboxylic acids to aryl substituted alpha-methoxystyrenes in water. In addition, we also demonstrate that the AIF-PI method can be used to systematically compute the exact value of zero-point energy (beyond the harmonic approximation) by simply minimizing the centroid effective potential.
Butko, Yana A. E-mail: kinderknecht@math.uni-sb.de; Grothaus, Martin; Smolyanov, Oleg G.
2016-02-15
Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures.
Geng, Yijia; Xu, Shuping; Xu, Weiqing; Chen, Lei; Chen, Gang; Bi, Wenbin; Cui, Haining
2015-05-15
An integrated and portable Raman analyzer featuring an inverted probe fixed on a motor-driving adjustable optical module was designed for the combination of a microfluidic system. It possesses a micro-imaging function. The inverted configuration is advantageous to locate and focus microfluidic channels. Different from commercial micro-imaging Raman spectrometers using manual switchable light path, this analyzer adopts a dichroic beam splitter for both imaging and signal collection light paths, which avoids movable parts and improves the integration and stability of optics. Combined with surface-enhanced Raman scattering technique, this portable Raman micro-analyzer is promising as a powerful tool for microfluidic analytics.
Vanícek, Jirí
2011-01-01
Nuclear tunneling and other nuclear quantum effects have been shown to play a significant role in molecules as large as enzymes even at physiological temperatures. I discuss how these quantum phenomena can be accounted for rigorously using Feynman path integrals in calculations of the equilibrium and kinetic isotope effects as well as of the temperature dependence of the rate constant. Because these calculations are extremely computationally demanding, special attention is devoted to increasing the computational efficiency by orders of magnitude by employing efficient path integral estimators.
NASA Astrophysics Data System (ADS)
Botelho, Luiz C. L.
2017-02-01
We present new path integral studies on the Polyakov noncritical and Nambu-Goto critical string theories and their applications to QCD(SU(∞)) interquark potential. We also evaluate the long distance asymptotic behavior of the interquark potential on the Nambu-Goto string theory with an extrinsic term in Polyakov’s string at D →∞. We also propose an alternative and a new view to covariant Polyakov’s string path integral with a fourth-order two-dimensional quantum gravity, is an effective stringy description for QCD(SU(∞)) at the deep infrared region.
A Path to Successful Energy Retrofits: Early Collaboration through Integrated Project Delivery Teams
Parrish, Kristen
2012-10-01
This document guides you through a process for the early design phases of retrofit projects to help you mitigate frustrations commonly experienced by building owners and designers. It outlines the value of forming an integrated project delivery team and developing a communication and information-sharing infrastructure that fosters collaboration. This guide does not present a complete process for designing an energy retrofit for a building. Instead, it focuses on the early design phase tasks related to developing and selecting energy efficiency measures (EEMs) that benefit from collaboration, and highlights the resulting advantages.
NASA Technical Reports Server (NTRS)
Taylor, B.
1990-01-01
The design of Integrated Circuits has evolved past the black art practiced by a few semiconductor companies to a world wide community of users. This was basically accomplished by the development of computer aided design tools which were made available to this community. As the tools matured into different components of the design task they were accepted into the community at large. However, the next step in this evolution is being ignored by the large tool vendors hindering the continuation of this process. With system level definition and simulation through the logic specification well understood, why is the physical generation so blatantly ignored. This portion of the development is still treated as an isolated task with information being passed from the designer to the layout function. Some form of result given back but it severely lacks full definition of what has transpired. The level of integration in I.C.'s for tomorrow, whether through new processes or applications will require higher speeds, increased transistor density, and non-digital performance which can only be achieved through attention to the physical implementation.
Motivated Cognition and Fairness: Insights, Integration, and Creating a Path Forward.
Barclay, Laurie J; Bashshur, Michael R; Fortin, Marion
2017-03-09
How do individuals form fairness perceptions? This question has been central to the fairness literature since its inception, sparking a plethora of theories and a burgeoning volume of research. To date, the answer to this question has been predicated on the assumption that fairness perceptions are subjective (i.e., "in the eye of the beholder"). This assumption is shared with motivated cognition approaches, which highlight the subjective nature of perceptions and the importance of viewing individuals arriving at those perceptions as active and motivated processors of information. Further, the motivated cognition literature has other key insights that have been less explicitly paralleled in the fairness literature, including how different goals (e.g., accuracy, directional) can influence how individuals process information and arrive at their perceptions. In this integrative conceptual review, we demonstrate how interpreting extant theory and research related to the formation of fairness perceptions through the lens of motivated cognition can deepen our understanding of fairness, including how individuals' goals and motivations can influence their subjective perceptions of fairness. We show how this approach can provide integration as well as generate new insights into fairness processes. We conclude by highlighting the implications that applying a motivated cognition perspective can have for the fairness literature and by providing a research agenda to guide the literature moving forward. (PsycINFO Database Record
NASA Astrophysics Data System (ADS)
Leontiev, Anton; Reuveni, Yuval
2017-02-01
Using GPS satellites signals, we can study different processes and coupling mechanisms that can help us understand the physical conditions in the lower atmosphere, which might lead or act as proxies for severe weather events such as extreme storms and flooding. GPS signals received by ground stations are multi-purpose and can also provide estimates of tropospheric zenith delays, which can be converted into accurate integrated water vapor (IWV) observations using collocated pressure and temperature measurements on the ground. Here, we present for the first time the use of Israel's dense regional GPS network for extracting tropospheric zenith path delays combined with near-real-time Meteosat-10 water vapor (WV) and surface temperature pixel intensity values (7.3 and 10.8 µm channels, respectively) in order to assess whether it is possible to obtain absolute IWV (kg m-2) distribution. The results show good agreement between the absolute values obtained from our triangulation strategy based solely on GPS zenith total delays (ZTD) and Meteosat-10 surface temperature data compared with available radiosonde IWV absolute values. The presented strategy can provide high temporal and special IWV resolution, which is needed as part of the accurate and comprehensive observation data integrated in modern data assimilation systems and is required for increasing the accuracy of regional numerical weather prediction systems forecast.
NASA Astrophysics Data System (ADS)
Sharma, Rati; Cherayil, Binny J.
2013-10-01
Gene expression in living systems is inherently stochastic, and tends to produce varying numbers of proteins over repeated cycles of transcription and translation. In this paper, an expression is derived for the steady-state protein number distribution starting from a two-stage kinetic model of the gene expression process involving p proteins and r mRNAs. The derivation is based on an exact path integral evaluation of the joint distribution, P(p,r,t), of p and r at time t, which can be expressed in terms of the coupled Langevin equations for p and r that represent the two-stage model in continuum form. The steady-state distribution of p alone, P(p), is obtained from P(p,r,t) (a bivariate Gaussian) by integrating out the r degrees of freedom and taking the limit t → ∞. P(p) is found to be proportional to the product of a Gaussian and a complementary error function. It provides a generally satisfactory fit to simulation data on the same two-stage process when the translational efficiency (a measure of intrinsic noise levels in the system) is relatively low; it is less successful as a model of the data when the translational efficiency (and noise levels) are high.
NASA Astrophysics Data System (ADS)
Kimizuka, Hajime; Ogata, Shigenobu
We investigated the H diffusivity in face-centered cubic Pd and Al by performing path-integral molecular dynamics (PIMD) modeling in the framework of density functional theory (DFT); in our calculations, we took nuclear quantum effects into consideration. The DFT results showed that the H-migration barriers (Em) in Pd and Al exhibited similar values (approximately 0.16 eV), while the H atoms were stable at octahedral (O) sites for Pd and at tetrahedral (T) sites for Al. The PIMD-based free-energy profiles for H migration between the O-site and T-site were evaluated using the thermodynamic integration of the centroid forces at 150-600 K. We confirmed that the quantum effects significantly affected the Em and the difference between the energies of the H atom at the O-site and the T-site (EO - T); The Em and EO - T values in Pd at 300 K increased by 32% and 98%, respectively, relative to the classical limit. On the other hand, the Em and ET - O (i.e., -EO - T) values in Al at 300 K decreased by 3% and 41%, respectively. This suggested that the quantum nature of H nuclei was essential for understanding the H-diffusion kinetics in these metals even above ambient temperature.
NASA Astrophysics Data System (ADS)
Mühlbacher, Lothar; Ankerhold, Joachim; Escher, Charlotte
2004-12-01
An improved real-time quantum Monte Carlo procedure is presented and applied to describe the electronic transfer dynamics along molecular chains. The model consists of discrete electronic sites coupled to a thermal environment which is integrated out exactly within the path integral formulation. The approach is numerically exact and its results reduce to known analytical findings (Marcus theory, golden rule) in proper limits. Special attention is paid to the role of superexchange and sequential hopping at lower temperatures in symmetric donor-bridge-acceptor systems. In contrast to previous approximate studies, superexchange turns out to play a significant role only for extremely high-lying bridges where the transfer is basically frozen or for extremely low temperatures where for weaker dissipation a description in terms of rate constants is no longer feasible. For bridges with increasing length an algebraic decrease of the yield is found for short as well as for long bridges. The approach can be extended to electronic systems with more complicated topologies including impurities and in presence of external time-dependent forces.
NASA Astrophysics Data System (ADS)
Gaspa, M. C.; De La Cruz, R. M.; Olfindo, N. T.; Borlongan, N. J. B.; Perez, A. M. C.
2016-10-01
Stream network delineation based on LiDAR-derived digital terrain model (DTM) may produce stream segments that are inexistent or incomplete because of limitations imposed by extraction procedure, terrain and data. The applicability of a common threshold value in defining streams such as those implemented through the D8 algorithm also remains in question because the threshold varies depending on the geomorphology of the area. Flat areas and improper hydrologic conditioning produce erratic stream network. To counteract these limitations, this study proposes a workflow that improves the stream network produced by the D8 algorithm. It incorporates user-defined channel initiation points as inputs to a tool developed to automatically trace the flow of water into the next actual stream segment. Spurious streams along digital dams and flat areas are also manually reshaped. The proposed workflow is implemented in Iligan River Basin, Philippines using LiDARderived DTM of 1-meter resolution. The Flow Path Tracing (FPT) method counteracts the limits imposed by extraction procedure, terrain and data. It is applicable to different typologies of watersheds by eliminating the need to use site-specific threshold in determining streams. FPT is implemented as a Phyton script to automate the tracing of the streams using the flow direction raster. The FPT method is compared to the blue line digitization and the D8 method using morphometric parameters, such as stream number, stream order and stream length, to assess its performance. Results show that streams derived from the FPT method has higher stream order, number and length. An accuracy of 93.5% produced from field validation of the FPT method's streams strengthens the findings that integrating manual channel head initiation and flow path tracing can be used for nationwide extraction of streams using LiDAR-derived-DTM in the Philippines.
Ecosystem services and integrated water resource management: different paths to the same end?
Cook, Brian R; Spray, Christopher J
2012-10-30
The two concepts that presently dominate water resource research and management are the Global Water Partnership's (GWP, 2000) interpretation of Integrated Water Resource Management (IWRM) and Ecosystem Services (ES) as interpreted by the Millennium Ecosystem Assessment (MA, 2005). Both concepts are subject to mounting criticism, with a significant number of critiques focusing on both their conceptual and methodological incompatibility with management and governance, what has come to be known as the 'implementation gap'. Emergent within the ES and IWRM literatures, then, are two parallel debates concerning the gap between conceptualisation and implementation. Our purpose for writing this review is to argue: 1) that IWRM and ES have evolved into nearly identical concepts, 2) that they face the same critical challenge of implementation, and 3) that, if those interested in water research and management are to have a positive impact on the sustainable utilisation of dwindling water resources, they must break the tendency to jump from concept to concept and confront the challenges that arise with implementation.
NASA Astrophysics Data System (ADS)
Fallon, J.; Han, Z. T.; Gross, B.; Moshary, F.
2013-12-01
Microwave Radiometers are mounted on satellites and the ground to collect climatological data. While they provide very useful information about temperature, RH, and water vapor, radiometers should periodically be cross-referenced with other instruments to gauge the veracity of the data. Data available from the closest ground-based GPS receivers and sun photometers was plotted alongside, and used to analyze, data from City College's Microwave Radiometer. Observing all of the data together in a graph allows one to see some of the general advantages and disadvantages of each instrument. The GPS-MET seems to be accurate continuously, while AERONET data is not even available during the night and while there is cloud cover. Lastly, the microwave radiometer collects data continuously, but at certain times the data are about five times higher than the expected values, based on the values given by GPS-MET and AERONET. A good explanation for those spikes is rainfall. For times when it is not raining, the microwave radiometer at City College is sufficiently close to the integrated water vapor data collected by City College's sun photometer and data from Union, New Jersey and East Moriches, New York, as proven by statistical tools.
NASA Astrophysics Data System (ADS)
Yong, Liu; Qichao, Hong; Lihua, Liang
1999-05-01
This paper presents an elasto-viscoplastic consistent tangent operator (CTO) based boundary element formulation, and application for calculation of path-domain independent J integrals (extension of the classical J integrals) in nonlinear crack analysis. When viscoplastic deformation happens, the effective stresses around the crack tip in the nonlinear region is allowed to exceed the loading surface, and the pure plastic theory is not suitable for this situation. The concept of consistency employed in the solution of increment viscoplastic problem, plays a crucial role in preserving the quadratic rate asymptotic convergence of iteractive schemes based on Newton's method. Therefore, this paper investigates the viscoplastic crack problem, and presents an implicit viscoplastic algorithm using the CTO concept in a boundary element framework for path-domain independent J integrals. Applications are presented with two numerical examples for viscoplastic crack problems and J integrals.
A Critical Path for Data Integration in the U.S. Earth Sciences
NASA Astrophysics Data System (ADS)
Gallagher, K. T.; Allison, M. L.
2011-12-01
Development efforts for the U.S. Geoscience Information Network (US GIN) have crystallized around the Community for Data Integration (CDI) at the USGS, and the 50-state AASG State Geothermal Data project. The next step in developing a USGS-AASG community is to bring these two efforts into closer alignment through greater participation in CDI activities by geoinformatics practitioners from state geological surveys, and implementation of test bed activities by the USGIN partners. Test bed activities in the geological survey community will define a scope and provide a foundation to promote the use of specifications developed by the larger geoinformatics community. Adoption of some of these specifications as 'standards' by USGS and AASG for use by those organizations will lend authority and motivate wider adoption. The arc from use case to test bed to production deployments to agreement on 'standard' specifications for data discovery and access must be propelled by active interest from the user communities who have a stake in the outcome. The specifications developed will benefit the organizations involved in development, testing and deployment, which motivates participation -- a model that has worked successfully for standards organizations such as OGC, ISO and OASIS. The governance structure to support such a community process should promote grass root nucleation of interest groups that are the core of development efforts. Some mechanism for community agreement on priorities is desirable because geological survey agencies will need to allocate resources to support development. Loosely knit organizations such as ESIP and the current CDI provide models for this kind of structure. Because many geological surveys have data archive and dissemination functions as part of their portfolio, some support for the system can be built into the operating expenses and overhead. Sharing of resources and reuse of components can reduce the cost. Wide adoption of similar software
NASA Astrophysics Data System (ADS)
Svoboda, Ondřej; Ončák, Milan; Slavíček, Petr
2011-10-01
We have performed large-scale simulations of UV absorption spectra of water clusters (monomer to octamer) using a combination of ab initio path-integral molecular dynamics with reflection principle. The aim of the present work is four-fold: (1) To explore the transition from isolated molecules to bulk water from the perspective of UV photoabsorption. (2) To investigate quantum nuclear and thermal effects on the shape of the water UV spectra. (3) To make an assessment of the density functional theory functionals to be used for water excited states. (4) To check the applicability of the QM/MM schemes for a description of the UV absorption. Within the path integral molecular dynamics (PIMD)/reflection principle approach both the thermal and quantum vibrational effects including anharmonicities are accounted for. We demonstrate that shape of the spectra is primarily controlled by the nuclear quantum effects. The excited states and transition characteristics of the water clusters were calculated with the time-dependent density functional theory and equation-of-motion coupled clusters singles and doubles methods. Based on our benchmark calculations considering the whole UV spectrum we argue that the BHandHLYP method performs best among the 6 functionals tested (B3LYP, BHandHLYP, BNL, CAM-B3LYP, LC-ωPBE, and M06HF). We observe a gradual blueshift of the maximum of the first absorption peak with the increasing cluster size. The UV absorption spectrum for the finite size clusters (i.e., the peak centers, peak widths, and photoabsorption cross section) essentially converges into the corresponding bulk water spectrum. The effect of distant molecules accounted for within the polarizable continuum model is shown to be almost negligible. Using the natural transition orbitals we demonstrate that the first absorption band is formed by localized excitations while the second band includes delocalized excited states. Consequently, the QM/MM electrostatic embedding scheme can only be
Moix, Jeremy M.; Ma, Jian; Cao, Jianshu
2015-03-07
A numerically exact path integral treatment of the absorption and emission spectra of open quantum systems is presented that requires only the straightforward solution of a stochastic differential equation. The approach converges rapidly enabling the calculation of spectra of large excitonic systems across the complete range of system parameters and for arbitrary bath spectral densities. With the numerically exact absorption and emission operators, one can also immediately compute energy transfer rates using the multi-chromophoric Förster resonant energy transfer formalism. Benchmark calculations on the emission spectra of two level systems are presented demonstrating the efficacy of the stochastic approach. This is followed by calculations of the energy transfer rates between two weakly coupled dimer systems as a function of temperature and system-bath coupling strength. It is shown that the recently developed hybrid cumulant expansion (see Paper II) is the only perturbative method capable of generating uniformly reliable energy transfer rates and emission spectra across a broad range of system parameters.
NASA Astrophysics Data System (ADS)
Ghosal, Aishani; Cherayil, Binny J.
2016-06-01
The Jarzynski relation (and its variants) has provided a route to the experimental evaluation of equilibrium free energy changes based on measurements conducted under arbitrary non-equilibrium conditions. Schroeder and co-workers [Soft Matter 10, 2178 (2014) and J. Chem. Phys. 141, 174903 (2014)] have recently exploited this fact to determine the elastic properties of model DNA from simulations and experiments of chain extension under elongational flow, bypassing the need to make these measurements mechanically using sophisticated optical trapping techniques. In this paper, motivated by these observations, we investigate chain elasticity analytically, using the Jarzynski relation and a finitely extensible nonlinear elastic-type Rouse model within a path integral formalism to calculate (essentially exactly) both the flow-induced free energy change between chain conformations of definite average end-to-end distance, as well as the force-extension curve that follows from it. This curve, based on a new analytic expression, matches the trends in the corresponding curve obtained from a model of chain stretching developed by Marko and Siggia [Macromolecules 28, 8759 (1995)], which itself is in very satisfactory agreement with the numerical and experimental data from the work of Schroeder et al.
Effect of the shape on the spin state and exchange in quantum dots. Feynman path integral analysis
Shevkunov, S. V.
2015-05-15
The ab initio computer simulation of the mixed quantum states of 1–5-nm model ellipsoid quantum dots with “soft” walls containing two and three quantum-indistinguishable nonrelativistic electrons has been performed by the path integral method. The calculation has been carried out beyond the single-electron and mean-field approximations with the fundamentally exact inclusion of Coulomb and exchange correlations of all orders and the spin variable. Distributions over the eigenfunctions of the spin-squared operator, as well as the equilibrium spin numbers, have been obtained depending on the shape of a quantum dot and the temperature. The complete set of basis functions symmetrized in permutations according to the spin of the system has been obtained by application of the Young symmetry operators. The dependence of the energy on the shape of the quantum dot corresponds to the negative sign of the surface tension at its boundary. The calculation indicates that the spin magnetic susceptibility in the system of two electrons decreases strongly for spherical quantum dots (“pairing” of spins) and the temperature dependences have a pronounced maximum whose position depends on the shape of the quantum dot. For three electrons in an oblate quantum dot, the inversion of the energy levels of spin states is observed and affects the spin magnetic susceptibility. The results indicate a strong dependence of the energy of collective spin states of electrons on the detailed inclusion of exchange and Coulomb spatial correlations.
Mudra, Regina; Douglas, Rodney J
2003-11-01
Classical Computer Science approaches to navigation by autonomous robots continue to make good progress. However, we have only a limited understanding of how navigation is implemented in the neural networks of animals, which still perform very much better in navigational tasks than robots. In this paper we explore the implementation of neural network based navigation in a simple robot. We use a modular navigation system that contains separate representations of visual input and the path integration process. These representations are combined to influence the behavior of a robot. Both representations are encoded within recurrent neuronal networks. The outputs of the representations are vectors of polar values that encode the location of the nearest object, or of a specific place in the environment. The robot manoeuvres in relation to these attended locations, in the context of its egocentric spatial map. During ego-motion towards a goal, the network representation of the goal moves in a counter-movement due to applied motor feedback. The robot's position is continuously compared against its visual input, and mismatches between the visually perceived goal position and its spatial representation are corrected.
Accurate path integral molecular dynamics simulation of ab-initio water at near-zero added cost
NASA Astrophysics Data System (ADS)
Elton, Daniel; Fritz, Michelle; Soler, José; Fernandez-Serra, Marivi
It is now established that nuclear quantum motion plays an important role in determining water's structure and dynamics. These effects are important to consider when evaluating DFT functionals and attempting to develop better ones for water. The standard way of treating nuclear quantum effects, path integral molecular dynamics (PIMD), multiplies the number of energy/force calculations by the number of beads, which is typically 32. Here we introduce a method whereby PIMD can be incorporated into a DFT molecular dynamics simulation at virtually zero cost. The method is based on the cluster (many body) expansion of the energy. We first subtract the DFT monomer energies, using a custom DFT-based monomer potential energy surface. The evolution of the PIMD beads is then performed using only the more-accurate Partridge-Schwenke monomer energy surface. The DFT calculations are done using the centroid positions. Various bead thermostats can be employed to speed up the sampling of the quantum ensemble. The method bears some resemblance to multiple timestep algorithms and other schemes used to speed up PIMD with classical force fields. We show that our method correctly captures some of key effects of nuclear quantum motion on both the structure and dynamics of water. We acknowledge support from DOE Award No. DE-FG02-09ER16052 (D.E.) and DOE Early Career Award No. DE-SC0003871 (M.V.F.S.).
NASA Astrophysics Data System (ADS)
Tramonto, F.; Salvestrini, P.; Nava, M.; Galli, D. E.
2015-07-01
By means of the Path Integral Monte Carlo method, we have performed a detailed microscopic study of 4He nanodroplets doped with an argon ion, Ar, at K. We have computed density profiles, energies, dissociation energies, and characterized the local order around the ion for nanodroplets with a number of 4He atoms ranging from 10 to 64 and also 128. We have found the formation of a stable solid structure around the ion, a "snowball", consisting of three concentric shells in which the 4He atoms are placed at the vertices of platonic solids: the first inner shell is an icosahedron (12 atoms); the second one is a dodecahedron with 20 atoms placed on the faces of the icosahedron of the first shell; the third shell is again an icosahedron composed of 12 atoms placed on the faces of the dodecahedron of the second shell. The "magic numbers" implied by this structure, 12, 32, and 44 helium atoms, have been observed in a recent experimental study (Bartl et al., J Phys Chem A 118:8050, 2014) of these complexes; the dissociation energy curve computed in the present work shows jumps in correspondence with those found in the nanodroplets abundance distribution measured in that experiment, strengthening the agreement between theory and experiment. The same structures were predicted in Galli et al. (J Phys Chem A 115:7300, 2011) in a study regarding Na+@4He when ; a comparison between Ar+@4He and Na+@4He complexes is also presented.
NASA Astrophysics Data System (ADS)
Wang, Lecheng; Xie, Daiqian
2012-08-01
We report finite temperature quantum mechanical simulations of structural and dynamical properties of ArN-CO2 clusters using a path integral Monte Carlo algorithm. The simulations are based on a newly developed analytical Ar-CO2 interaction potential obtained by fitting ab initio results to an anisotropic two-dimensional Morse/Long-range function. The calculated distributions of argon atoms around the CO2 molecule in ArN-CO2 clusters with different sizes are consistent to the previous studies of the configurations of the clusters. A first-order perturbation theory is used to quantitatively predict the CO2 vibrational frequency shift in different clusters. The first-solvation shell is completed at N = 17. Interestingly, our simulations for larger ArN-CO2 clusters showed several different structures of the argon shell around the doped CO2 molecule. The observed two distinct peaks (2338.8 and 2344.5 cm-1) in the υ3 band of CO2 may be due to the different arrangements of argon atoms around the dopant molecule.
Moix, Jeremy M; Ma, Jian; Cao, Jianshu
2015-03-07
A numerically exact path integral treatment of the absorption and emission spectra of open quantum systems is presented that requires only the straightforward solution of a stochastic differential equation. The approach converges rapidly enabling the calculation of spectra of large excitonic systems across the complete range of system parameters and for arbitrary bath spectral densities. With the numerically exact absorption and emission operators, one can also immediately compute energy transfer rates using the multi-chromophoric Förster resonant energy transfer formalism. Benchmark calculations on the emission spectra of two level systems are presented demonstrating the efficacy of the stochastic approach. This is followed by calculations of the energy transfer rates between two weakly coupled dimer systems as a function of temperature and system-bath coupling strength. It is shown that the recently developed hybrid cumulant expansion (see Paper II) is the only perturbative method capable of generating uniformly reliable energy transfer rates and emission spectra across a broad range of system parameters.
NASA Technical Reports Server (NTRS)
Pliutau, Denis; Prasad, Narasimha S.
2012-01-01
In this paper a modeling method based on data reductions is investigated which includes pre analyzed MERRA atmospheric fields for quantitative estimates of uncertainties introduced in the integrated path differential absorption methods for the sensing of various molecules including CO2. This approach represents the extension of our existing lidar modeling framework previously developed and allows effective on- and offline wavelength optimizations and weighting function analysis to minimize the interference effects such as those due to temperature sensitivity and water vapor absorption. The new simulation methodology is different from the previous implementation in that it allows analysis of atmospheric effects over annual spans and the entire Earth coverage which was achieved due to the data reduction methods employed. The effectiveness of the proposed simulation approach is demonstrated with application to the mixing ratio retrievals for the future ASCENDS mission. Independent analysis of multiple accuracy limiting factors including the temperature, water vapor interferences, and selected system parameters is further used to identify favorable spectral regions as well as wavelength combinations facilitating the reduction in total errors in the retrieved XCO2 values.
Nagashima, H.; Tsuda, S.; Tsuboi, N.; Koshi, M.; Hayashi, K. A.; Tokumasu, T.
2014-04-07
In this paper, we describe the analysis of the thermodynamic properties of cryogenic hydrogen using classical molecular dynamics (MD) and path integral MD (PIMD) method to understand the effects of the quantum nature of hydrogen molecules. We performed constant NVE MD simulations across a wide density–temperature region to establish an equation of state (EOS). Moreover, the quantum effect on the difference of molecular mechanism of pressure–volume–temperature relationship was addressed. The EOS was derived based on the classical mechanism idea only using the MD simulation results. Simulation results were compared with each MD method and experimental data. As a result, it was confirmed that although the EOS on the basis of classical MD cannot reproduce the experimental data of saturation property of hydrogen in the high-density region, the EOS on the basis of PIMD well reproduces those thermodynamic properties of hydrogen. Moreover, it was clarified that taking quantum effects into account makes the repulsion force larger and the potential well shallower. Because of this mechanism, the intermolecular interaction of hydrogen molecules diminishes and the virial pressure increases.
Mavri, Janez; Matute, Ricardo A; Chu, Zhen T; Vianello, Robert
2016-04-14
Brain monoamines regulate many centrally mediated body functions, and can cause adverse symptoms when they are out of balance. A starting point to address challenges raised by the increasing burden of brain diseases is to understand, at atomistic level, the catalytic mechanism of an essential amine metabolic enzyme-monoamine oxidase B (MAO B). Recently, we demonstrated that the rate-limiting step of MAO B catalyzed conversion of amines into imines represents the hydride anion transfer from the substrate α-CH2 group to the N5 atom of the flavin cofactor moiety. In this article we simulated for MAO B catalyzed dopamine decomposition the effects of nuclear tunneling by the calculation of the H/D kinetic isotope effect. We applied path integral quantization of the nuclear motion for the methylene group and the N5 atom of the flavin moiety in conjunction with the QM/MM treatment on the empirical valence bond (EVB) level for the rest of the enzyme. The calculated H/D kinetic isotope effect of 12.8 ± 0.3 is in a reasonable agreement with the available experimental data for closely related biogenic amines, which gives strong support for the proposed hydride mechanism. The results are discussed in the context of tunneling in enzyme centers and advent of deuterated drugs into clinical practice.
NASA Technical Reports Server (NTRS)
Abshire, James B.; Riris, Haris; Weaver, Clark J.; Mao, Jianping; Allan, Graham R.; Hasselbrack, William E.; Browell, Edward V.
2013-01-01
We report on airborne CO2 column absorption measurements made in 2009 with a pulsed direct-detection lidar operating at 1572.33 nm and utilizing the integrated path differential absorption technique. We demonstrated these at different altitudes from an aircraft in July and August in flights over four locations in the central and eastern United States. The results show clear CO2 line shape and absorption signals, which follow the expected changes with aircraft altitude from 3 to 13 km. The lidar measurement statistics were also calculated for each flight as a function of altitude. The optical depth varied nearly linearly with altitude, consistent with calculations based on atmospheric models. The scatter in the optical depth measurements varied with aircraft altitude as expected, and the median measurement precisions for the column varied from 0.9 to 1.2 ppm. The altitude range with the lowest scatter was 810 km, and the majority of measurements for the column within it had precisions between 0.2 and 0.9 ppm.
NASA Astrophysics Data System (ADS)
Volkoff, Tyler; Kwon, Yongkyung; Whaley, K. Birgitta
2016-10-01
We present a path integral Monte Carlo study of the global superfluid fraction and local superfluid density in cylindrically symmetric reservoirs of liquid 4He separated by nanoaperture arrays. The superfluid response to both translations along the axis of symmetry (longitudinal response) and rotations about the cylinder axis (transverse response) are computed, together with radial and axial density distributions that reveal the microscopic inhomogeneity arising from the combined effects of the confining external potential and the 4He-4He interatomic potentials. We make a microscopic determination of the length scale of decay of superfluidity at the radial boundaries of the system by analyzing the local superfluid density distribution to extract a displacement length that quantifies the superfluid mass displacement away from the boundary. We find that the longitudinal superfluid response is reduced in reservoirs separated by a septum containing sufficiently small apertures compared to a cylinder with no intervening aperture array, for all temperatures below Tλ. For a single aperture in the septum, a significant drop in the longitudinal superfluid response is seen when the aperture diameter is made smaller than twice the empirical temperature-dependent 4He healing length, consistent with the formation of a weak link between the reservoirs. Increasing the diameter of a single aperture or the number of apertures in the array results in an increase of the superfluid density toward the expected bulk value.
NASA Astrophysics Data System (ADS)
Walker, Brent; Michaelides, Angelos
2010-11-01
The impact of quantum nuclear effects on hydrogen (H-) bond strength has been inferred in earlier work from bond lengths obtained from path integral molecular dynamics (PIMD) simulations. To obtain a direct quantitative assessment of such effects, we use constrained-centroid PIMD simulations to calculate the free energy changes upon breaking the H-bonds in dimers of HF and water. Comparing ab initio simulations performed using PIMD and classical nucleus molecular dynamics (MD), we find smaller dissociation free energies with the PIMD method. Specifically, at 50 K, the H-bond in (HF)2 is about 30% weaker when quantum nuclear effects are included, while that in (H2O)2 is about 15% weaker. In a complementary set of simulations, we compare unconstrained PIMD and classical nucleus MD simulations to assess the influence of quantum nuclei on the structures of these systems. We find increased heavy atom distances, indicating weakening of the H-bond consistent with that observed by direct calculation of the free energies of dissociation.
NASA Astrophysics Data System (ADS)
Krajewski, Florian R.; Müser, Martin H.
2005-03-01
The commensurate Frenkel Kontorova (FK) model is studied using path-integral molecular dynamics (PIMD). We focus on the highly discrete case, in which the embedding potential has a much greater maximum curvature than the harmonic potential connecting two particles in the FK chain. When efficient sampling methods are used, the dynamical interpretation of adiabatic PIMD appears to represent quite accurately the true time correlation functions of this highly correlated many-body system. We have found that the discrete, quantum FK model shows different behavior than its continuum version. The spectral density does not show the characteristic ω-2Θ(ω-ωc) cusp of the continuum solution in the pinned phase (m>mc). We also identify a dynamical quantum hysteresis in addition to the regular classical hysteresis when an external force is applied to the FK chain. In the unpinned phase (m⩽mc), we find a linear response damping coefficient which is finite and only weakly dependent on temperature T at small values of T.
NASA Astrophysics Data System (ADS)
Ehret, Gerhard; Flamant, Pierre; Ciais, Philippe; Fabien, Gibert; Amediek, Axel; Kiemle, Christoph; Fix, Andreas; Quatrevalet, Mathieu; Wirth, Martin
Atmospheric methane (CH4) is a powerful greenhouse gas, which has a Greenhouse Warming Potential (GWP) of 25 relative to CO2 on a time scale of 100 years. Despite the fact that the imbalance between the sources and sinks has decreased in the early 1990's to an insignificant value, a significant renewal of the CH4 growth is reported in recent years. Questions arise whether an increase of atmospheric CH4 might be fostered through melting of permafrost soil in the Arctic region or arise from changes of the tropical wetlands which comprise the biggest natural methane source. Another reason could be the change in the agro-industrial era of predominant human influence or the very large deposits of CH4 as gas hydrates on ocean shelves that are vulnerable to ocean warming. The French-German Climate Monitoring Initiative, which has recently been selected to undergo Phase0/A studies in a joint project by the space agencies CNES (France)and DLR (Germany), targets on satellite observations of atmospheric CH4 for the improvement of our knowledge on regional to synoptic scale CH4 sources on a global basis. As a novel feature, the observational instrument of this mission will be an Integrated Path Differential-Absorption (IPDA) Lidar system embarked on board of the French Myriade platform for the measurement of the column-weighted dry-air mixing ratio of CH4 in a nadir viewing configuration. This data will be provided by the lidar technique with no bias due to particles scattering in the light path and can directly be used as input for flux inversion models. In our presentation we will discuss the observational principle and the sampling strategy of the envisaged mission in connection to the needs for CH4 flux inversion experiments. In addition, we report on supporting campaign activities on airborne measurements of Lidar reflectivity data in the respective spectral region. The airborne data is of prime interest for the generation of pseudo CH4 data examples using the satellite
NASA Astrophysics Data System (ADS)
Drozdov, Alexander N.; Talkner, Peter
1998-08-01
Fokker-Planck processes with a singular diffusion matrix are quite frequently met in Physics and Chemistry. For a long time the resulting noninvertability of the diffusion matrix has been looked as a serious obstacle for treating these Fokker-Planck equations by various powerful numerical methods of quantum and statistical mechanics. In this paper, a path-integral method is presented that takes advantage of the singularity of the diffusion matrix and allows one to solve such problems in a simple and economic way. The basic idea is to split the Fokker-Planck equation into one of a linear system and an anharmonic correction and then to employ a symmetric decomposition of the short time propagator, which is exact up to a high order in the time step. Just because of the singularity of the diffusion matrix, the factors of the resulting product formula consist of well behaved propagators. In this way one obtains a highly accurate propagation scheme, which is simultaneously fast, stable, and computationally simple. Because it allows much larger time steps, it is more efficient than the standard propagation scheme based on the Trotter splitting formula. The proposed method is tested for Brownian motion in different types of potentials. For a harmonic potential we compare to the known analytic results. For a symmetric double well potential we determine the transition rates between the two wells for different friction strengths and compare them with the crossover theories of Mel'nikov and Meshkov and Pollak, Grabert, and Hänggi. Using a properly defined energy loss of the deterministic particle dynamics, we obtain excellent agreement. The methodology is outlined for a large class of processes defined by generalized Langevin equations and processes driven by colored noise.
NASA Astrophysics Data System (ADS)
Lindoy, Lachlan P.; Kolmann, Stephen J.; D'Arcy, Jordan H.; Crittenden, Deborah L.; Jordan, Meredith J. T.
2015-11-01
Finite temperature quantum and anharmonic effects are studied in H2-Li+-benzene, a model hydrogen storage material, using path integral Monte Carlo (PIMC) simulations on an interpolated potential energy surface refined over the eight intermolecular degrees of freedom based upon M05-2X/6-311+G(2df,p) density functional theory calculations. Rigid-body PIMC simulations are performed at temperatures ranging from 77 K to 150 K, producing both quantum and classical probability density histograms describing the adsorbed H2. Quantum effects broaden the histograms with respect to their classical analogues and increase the expectation values of the radial and angular polar coordinates describing the location of the center-of-mass of the H2 molecule. The rigid-body PIMC simulations also provide estimates of the change in internal energy, ΔUads, and enthalpy, ΔHads, for H2 adsorption onto Li+-benzene, as a function of temperature. These estimates indicate that quantum effects are important even at room temperature and classical results should be interpreted with caution. Our results also show that anharmonicity is more important in the calculation of U and H than coupling—coupling between the intermolecular degrees of freedom becomes less important as temperature increases whereas anharmonicity becomes more important. The most anharmonic motions in H2-Li+-benzene are the "helicopter" and "ferris wheel" H2 rotations. Treating these motions as one-dimensional free and hindered rotors, respectively, provides simple corrections to standard harmonic oscillator, rigid rotor thermochemical expressions for internal energy and enthalpy that encapsulate the majority of the anharmonicity. At 150 K, our best rigid-body PIMC estimates for ΔUads and ΔHads are -13.3 ± 0.1 and -14.5 ± 0.1 kJ mol-1, respectively.
Whitfield, Troy W; Martyna, Glenn J
2007-02-21
In the effort to develop atomistic models capable of accurately describing nanoscale systems with complex interfaces, it has become clear that simple treatments with rigid charge distributions and dispersion coefficients selected to generate bulk properties are insufficient to predict important physical properties. The quantum Drude oscillator model, a system of one-electron pseudoatoms whose "pseudoelectrons" are harmonically bound to their respective "pseudonuclei," is capable of treating many-body polarization and dispersion interactions in molecular systems on an equal footing due to the ability of the pseudoatoms to mimic the long-range interactions that characterize real materials. Using imaginary time path integration, the Drude oscillator model can, in principle, be solved in computer operation counts that scale linearly with the number of atoms in the system. In practice, however, standard expressions for the energy and pressure, including the commonly used virial estimator, have extremely large variances that require untenably long simulation times to generate converged averages. In this paper, low-variance estimators for the internal energy are derived, in which the large zero-point energy of the oscillators does not contribute to the variance. The new estimators are applicable to any system of harmonic oscillators coupled to one another (or to the environment) via an arbitrary set of anharmonic interactions. The variance of the new estimators is found to be much smaller than standard estimators in three example problems, a one-dimensional anharmonic oscillator and quantum Drude models of the xenon dimer and solid (fcc) xenon, respectively, yielding 2-3 orders of magnitude improvement in computational efficiency.
VORHEES, CHARLES V.; SCHAEFER, TORI L.; WILLIAMS, MICHAEL T.
2010-01-01
We previously demonstrated that postnatal day 11–20 ±3,4-methylenedioxymethamphetamine (MDMA) exposure reduces locomotor activity and impairs path integration and spatial learning independent of the effects on activity. The effects were seen when the drug was administered twice per day, but the optimal dosing regimen is unknown. We tested whether the same total daily dose of MDMA administered in different patterns would equally affect later behavior. A split-litter design (15 litters) was used with one male/female pair per litter receiving one of four treatment regimens. All offspring received four injections per day on P11–20 as follows: 40 × 1 (40 mg/kg MDMA × 1 + saline × 3), 20 × 2 (20 mg/kg MDMA × 2 + saline × 2), 10 × 4 (10 mg/kg MDMA × 4), or Saline (saline × 4). Does were spaced 2 h apart. Group 40 × 1 received MDMA as the first daily dose followed by three saline doses; group 20 × 2 received MDMA as the first and last dose and saline for the middle two doses; group 10 × 4 received MDMA for all four doses; and the saline group received saline for all four doses. Regardless of dose schedule, all groups treated with MDMA exhibited reduced locomotor activity. No MDMA effects were found on swimming ability in a straight channel. Modest MDMA effects were found on Barnes maze performance. The major findings were that the 40 × 1 and 20 × 2 MDMA groups showed impaired Cincinnati multiple T-water-maze learning and the 10 × 4 and 20 × 2 MDMA groups showed impaired Morris water maze learning. The results suggest that MDMA dose distribution has a long-term differential effect on different types of learning. Dose distribution warrants greater attention in the design of developmental drug studies along with the standard considerations of dose and age. PMID:17415794
NASA Astrophysics Data System (ADS)
Pinilla, Carlos; Blanchard, Marc; Balan, Etienne; Natarajan, Suresh K.; Vuilleumier, Rodolphe; Mauri, Francesco
2015-08-01
The theoretical determination of the isotopic fractionation between an aqueous solution and a mineral is of utmost importance in Earth sciences. While for crystals, it is well established that equilibrium isotopic fractionation factors can be calculated using a statistical thermodynamic approach based on the vibrational properties, several theoretical methods are currently used to model ions in aqueous solution. In this work, we present a systematic study to determine the reduced partition function ratio (β-factor) of aqueous Mg2+ using several levels of theory within the simulations. In particular, using an empirical force field, we compare and discuss the performance of the exact results obtained from path integral molecular dynamics (PIMD) simulations, with respect to the more traditional methods based on vibrational properties and the cluster approximation. The results show the importance of including configurational disorder for the estimation of the equilibrium isotope fractionation factor. We also show that using the vibrational frequencies computed from snapshots taken from equilibrated classical molecular dynamics represents a good approximation for the study of aqueous ions. Based on these conclusions, the β-factor of aqueous Mg2+ have been estimated from a Car-Parrinello molecular dynamics (CPMD) simulation with an ab initio force field, and combined with the β-factors of carbonate minerals (magnesite, dolomite, calcite and aragonite). Mg β-factor of Mg-bearing aragonite, calculated here for the first time, displays a lower value than the three other carbonate minerals. This is explained by a strong distortion of the cationic site leading to a decrease of the coordination number during Ca-Mg substitution. Overall, the equilibrium magnesium isotope fractionation factors between aqueous Mg2+ and carbonate minerals that derive from this methodological study support the previous theoretical results obtained from embedded cluster models.
NASA Astrophysics Data System (ADS)
Oba, Yuki; Kawatsu, Tsutomu; Tachikawa, Masanori
2016-08-01
The on-the-fly ab initio density functional path integral molecular dynamics (PIMD) simulations, which can account for both the nuclear quantum effect and thermal effect, were carried out to evaluate the structures and "reduced" isotropic hyperfine coupling constants (HFCCs) for muoniated and hydrogenated acetone radicals (2-muoxy-2-propyl and 2-hydoxy-2-propyl) in vacuo. The reduced HFCC value from a simple geometry optimization calculation without both the nuclear quantum effect and thermal effect is -8.18 MHz, and that by standard ab initio molecular dynamics simulation with only the thermal effect and without the nuclear quantum effect is 0.33 MHz at 300 K, where these two methods cannot distinguish the difference between muoniated and hydrogenated acetone radicals. In contrast, the reduced HFCC value of the muoniated acetone radical by our PIMD simulation is 32.1 MHz, which is about 8 times larger than that for the hydrogenated radical of 3.97 MHz with the same level of calculation. We have found that the HFCC values are highly correlated with the local molecular structures; especially, the Mu—O bond length in the muoniated acetone radical is elongated due to the large nuclear quantum effect of the muon, which makes the expectation value of the HFCC larger. Although our PIMD result calculated in vacuo is about 4 times larger than the measured experimental value in aqueous solvent, the ratio of these HFCC values between muoniated and hydrogenated acetone radicals in vacuo is in reasonable agreement with the ratio of the experimental values in aqueous solvent (8.56 MHz and 0.9 MHz); the explicit presence of solvent molecules has a major effect on decreasing the reduced muon HFCC of in vacuo calculations for the quantitative reproduction.
NASA Astrophysics Data System (ADS)
Svoboda, Ondřej; Ončák, Milan; Slavíček, Petr
2011-10-01
We have applied ab initio based reflection principle to simulate photoelectron spectra of small water clusters, ranging from monomer to octamer. The role of quantum and thermal effects on the structure of the water photoelectron spectra is discussed within the ab initio path integral molecular dynamics (PIMD) framework. We have used the PIMD method with up to 40 beads to sample the ground state quantum distribution at temperature T = 180 K. We have thoroughly tested the performance of various density functionals (B3LYP, BHandHLYP, M06HF, BNL, LC-ωPBE, and CAM-B3LYP) for the ionization process description. The benchmarking based on a comparison of simulated photoelectron spectra to experimental data and high level equation-of-motion ionization potential coupled clusters with singles and doubles calculations has singled out the BHandHLYP and LC-ωPBE functionals as the most reliable ones for simulations of light induced processes in water. The good performance of the density functional theory functionals to model the water photoelectron spectra also reflects their ability to reliably describe open shell excited states. The width of the photoelectron spectrum converges quickly with the cluster size as it is controlled by specific interactions of local character. The peak position is, on the other hand, defined by long-range non-specific solvent effects; it therefore only slowly converges to the corresponding bulk value. We are able to reproduce the experimental valence photoelectron spectrum of liquid water within the combined model of the water octamer embedded in a polarizable dielectric continuum. We demonstrate that including the long-range polarization and the state-specific treatment of the solvent response are needed for a reliable liquid water ionization description.
Refaat, Tamer F; Singh, Upendra N; Yu, Jirong; Petros, Mulugeta; Remus, Ruben; Ismail, Syed
2016-05-20
Field experiments were conducted to test and evaluate the initial atmospheric carbon dioxide (CO_{2}) measurement capability of airborne, high-energy, double-pulsed, 2-μm integrated path differential absorption (IPDA) lidar. This IPDA was designed, integrated, and operated at the NASA Langley Research Center on-board the NASA B-200 aircraft. The IPDA was tuned to the CO_{2} strong absorption line at 2050.9670 nm, which is the optimum for lower tropospheric weighted column measurements. Flights were conducted over land and ocean under different conditions. The first validation experiments of the IPDA for atmospheric CO_{2} remote sensing, focusing on low surface reflectivity oceanic surface returns during full day background conditions, are presented. In these experiments, the IPDA measurements were validated by comparison to airborne flask air-sampling measurements conducted by the NOAA Earth System Research Laboratory. IPDA performance modeling was conducted to evaluate measurement sensitivity and bias errors. The IPDA signals and their variation with altitude compare well with predicted model results. In addition, off-off-line testing was conducted, with fixed instrument settings, to evaluate the IPDA systematic and random errors. Analysis shows an altitude-independent differential optical depth offset of 0.0769. Optical depth measurement uncertainty of 0.0918 compares well with the predicted value of 0.0761. IPDA CO_{2} column measurement compares well with model-driven, near-simultaneous air-sampling measurements from the NOAA aircraft at different altitudes. With a 10-s shot average, CO_{2} differential optical depth measurement of 1.0054±0.0103 was retrieved from a 6-km altitude and a 4-GHz on-line operation. As compared to CO_{2} weighted-average column dry-air volume mixing ratio of 404.08 ppm, derived from air sampling, IPDA measurement resulted in a value of 405.22±4.15 ppm with 1.02% uncertainty and
NASA Astrophysics Data System (ADS)
Durlak, Piotr; Latajka, Zdzisław
2010-10-01
Theoretical studies of the structure and proton motion in the intramolecular O-H…O hydrogen bonds in 2-acetyl-1,8-dihydroxy-3,6-dimethylnapthlane were carried out at the DFT and molecular dynamics levels. Geometry optimization at the PBE1PBE/6-311++G(2d,2p) level demonstrate the existence of two tautomers on the potential energy surface. Dynamics of proton motion in intramolecular hydrogen bonds was investigated in vacuo at 100 K using Car-Parrinello and path integral molecular dynamics. For the strong intramolecular hydrogen bond very large delocalization of bridging proton is noted, especially in the path integral simulation where quantum effects are taken into account. No tautomerism was found for this intramolecular hydrogen bond.
NASA Astrophysics Data System (ADS)
Durlak, Piotr; Latajka, Zdzisław; Berski, Sławomir
2009-07-01
Lithium bonding in lithium 2-pyridyl-N-oxide acetate has been investigated using classic Car-Parrinello molecular dynamics (CPMD) and the path integral approach [path integrals molecular dynamics (PIMD)]. The simulations have been performed in 300 K. Structures, energies, and lithium trajectories have been determined. The CPMD results show that the lithium atom is generally equidistant between heavy atoms in the (O⋯Li⋯O) bridge. Applying quantum effects through the PIMD leads to similar conclusion. The theoretical lithium 2-pyridyl-N-oxide acetate infrared spectrum has also been determined using the CPMD calculations. This shows very good agreement with available experimental results and reproduces well the broad low-frequency band observed experimentally. In order to gain deeper understanding of the nature of the lithium bonding topological analysis of the electron localization function has been applied.
NASA Astrophysics Data System (ADS)
Kim, Dongsup; Doll, J. D.; Gubernatis, J. E.
1997-01-01
Vibrational line shapes for a hydrogen atom on an embedded atom model (EAM) of the Ni(111) surface are extracted from path integral Monte Carlo data. Maximum entropy methods are utilized to stabilize this inversion. Our results indicate that anharmonic effects are significant, particularly for vibrational motion parallel to the surface. Unlike their normal mode analogs, calculated quantum line shapes for the EAM potential predict the correct ordering of vibrational features corresponding to parallel and perpendicular adsorbate motion.
Rigdon, J. Brian; Smith, Marcus Daniel; Mulder, Samuel A
2014-01-07
PathFinder is a graph search program, traversing a directed cyclic graph to find pathways between labeled nodes. Searches for paths through ordered sequences of labels are termed signatures. Determining the presence of signatures within one or more graphs is the primary function of Path Finder. Path Finder can work in either batch mode or interactively with an analyst. Results are limited to Path Finder whether or not a given signature is present in the graph(s).
Mielke, Steven L; Truhlar, Donald G
2015-01-28
We present an improved version of our "path-by-path" enhanced same path extrapolation scheme for Feynman path integral (FPI) calculations that permits rapid convergence with discretization errors ranging from O(P(-6)) to O(P(-12)), where P is the number of path discretization points. We also present two extensions of our importance sampling and stratified sampling schemes for calculating vibrational-rotational partition functions by the FPI method. The first is the use of importance functions for dihedral angles between sets of generalized Jacobi coordinate vectors. The second is an extension of our stratification scheme to allow some strata to be defined based only on coordinate information while other strata are defined based on both the geometry and the energy of the centroid of the Feynman path. These enhanced methods are applied to calculate converged partition functions by FPI methods, and these results are compared to ones obtained earlier by vibrational configuration interaction (VCI) calculations, both calculations being for the Jordan-Gilbert potential energy surface. The earlier VCI calculations are found to agree well (within ∼1.5%) with the new benchmarks. The FPI partition functions presented here are estimated to be converged to within a 2σ statistical uncertainty of between 0.04% and 0.07% for the given potential energy surface for temperatures in the range 300-3000 K and are the most accurately converged partition functions for a given potential energy surface for any molecule with five or more atoms. We also tabulate free energies, enthalpies, entropies, and heat capacities.
NASA Astrophysics Data System (ADS)
Nahri, Davoud G.; Mathkoor, Faisal H. A.; Ooi, C. H. Raymond
2017-02-01
A dissipative quantum dot (QD)-cavity system, where the QD is initially prepared in the excited state with no photon in the cavity, coupled to a longitudinal acoustic (LA) phonon reservoir is studied using a numerically exact real-time path-integral approach. Three distinct dynamical regimes of weak (WC), strong (SC), and coherent coupling (CC) are discussed and more accurate conditions identifying them are presented. Our results show that to have the CC regime, which is characterized by clear vacuum Rabi oscillation (VRO), vacuum Rabi splitting (VRS) should be larger than the sum of the widths of the corresponding peaks. In order to distinguish between contributions of population decay and impure dephasing, induced by LA phonon bath and the dissipations, we propose a two-part phenomenological expression, corresponding to the population decay and impure dephasing, which fits the QD-cavity decay curves perfectly and is used to calculate the corresponding spectra. We demonstrate that the effective population decay rate (the emission rate) increases from the carrier recombination rate to a maximum value, which is the mean of the QD and cavity dissipation rates, with QD-cavity coupling strength. To study the role of the effective impure dephasing rate on the width of the central peak of the spectra we introduce a quantity that can also be applied in determining the distinct coupling regimes. This quantity enables us to identify the onset of the SC regime as the point where the impure dephasing term begins to contribute to the central band of the spectrum significantly, as a result of the existence of VRO with a very small frequency (unclear VRO) at the corresponding decay curve. Its contribution to the width of the central peak increases with the coupling strength up to the onset of the CC regime, then reduces as a result of the appearance of sidebands in the spectra, which originates from clear VRO. The effective population decay and impure dephasing rate contribute
Nahri, Davoud G; Mathkoor, Faisal H A; Raymond Ooi, C H
2017-02-08
A dissipative quantum dot (QD)-cavity system, where the QD is initially prepared in the excited state with no photon in the cavity, coupled to a longitudinal acoustic (LA) phonon reservoir is studied using a numerically exact real-time path-integral approach. Three distinct dynamical regimes of weak (WC), strong (SC), and coherent coupling (CC) are discussed and more accurate conditions identifying them are presented. Our results show that to have the CC regime, which is characterized by clear vacuum Rabi oscillation (VRO), vacuum Rabi splitting (VRS) should be larger than the sum of the widths of the corresponding peaks. In order to distinguish between contributions of population decay and impure dephasing, induced by LA phonon bath and the dissipations, we propose a two-part phenomenological expression, corresponding to the population decay and impure dephasing, which fits the QD-cavity decay curves perfectly and is used to calculate the corresponding spectra. We demonstrate that the effective population decay rate (the emission rate) increases from the carrier recombination rate to a maximum value, which is the mean of the QD and cavity dissipation rates, with QD-cavity coupling strength. To study the role of the effective impure dephasing rate on the width of the central peak of the spectra we introduce a quantity that can also be applied in determining the distinct coupling regimes. This quantity enables us to identify the onset of the SC regime as the point where the impure dephasing term begins to contribute to the central band of the spectrum significantly, as a result of the existence of VRO with a very small frequency (unclear VRO) at the corresponding decay curve. Its contribution to the width of the central peak increases with the coupling strength up to the onset of the CC regime, then reduces as a result of the appearance of sidebands in the spectra, which originates from clear VRO. The effective population decay and impure dephasing rate contribute
NASA Astrophysics Data System (ADS)
Singh, Upendra N.; Petros, Mulugeta; Refaat, Tamer F.; Yu, Jirong
2016-05-01
For more than 15 years, NASA Langley Research Center (LaRC) has contributed in developing several 2-micron carbon dioxide active remote sensors using the DIAL technique. Currently, an airborne 2-micron triple-pulse integrated path differential absorption (IPDA) lidar is under development at NASA LaRC. This paper focuses on the advancement of the 2-micron triple-pulse IPDA lidar development. Updates on the state-of-the-art triple-pulse laser transmitter will be presented including the status of wavelength control, packaging and lidar integration. In addition, receiver development updates will also be presented, including telescope integration, detection systems and data acquisition electronics. Future plan for IPDA lidar system for ground integration, testing and flight validation will be presented.
NASA Technical Reports Server (NTRS)
Singh, Upendra N.; Petros, Mulugeta; Refaat, Tamer F.; Yu, Jirong
2016-01-01
For more than 15 years, NASA Langley Research Center (LaRC) has contributed in developing several 2-micron carbon dioxide active remote sensors using the DIAL technique. Currently, an airborne 2-micron triple-pulse integrated path differential absorption (IPDA) lidar is under development at NASA LaRC. This paper focuses on the advancement of the 2-micron triple-pulse IPDA lidar development. Updates on the state-of-the-art triple-pulse laser transmitter will be presented including the status of wavelength control, packaging and lidar integration. In addition, receiver development updates will also be presented, including telescope integration, detection systems and data acquisition electronics. Future plan for IPDA lidar system for ground integration, testing and flight validation will be presented.
Mielke, Steven L. E-mail: truhlar@umn.edu; Truhlar, Donald G. E-mail: truhlar@umn.edu
2015-01-28
We present an improved version of our “path-by-path” enhanced same path extrapolation scheme for Feynman path integral (FPI) calculations that permits rapid convergence with discretization errors ranging from O(P{sup −6}) to O(P{sup −12}), where P is the number of path discretization points. We also present two extensions of our importance sampling and stratified sampling schemes for calculating vibrational–rotational partition functions by the FPI method. The first is the use of importance functions for dihedral angles between sets of generalized Jacobi coordinate vectors. The second is an extension of our stratification scheme to allow some strata to be defined based only on coordinate information while other strata are defined based on both the geometry and the energy of the centroid of the Feynman path. These enhanced methods are applied to calculate converged partition functions by FPI methods, and these results are compared to ones obtained earlier by vibrational configuration interaction (VCI) calculations, both calculations being for the Jordan–Gilbert potential energy surface. The earlier VCI calculations are found to agree well (within ∼1.5%) with the new benchmarks. The FPI partition functions presented here are estimated to be converged to within a 2σ statistical uncertainty of between 0.04% and 0.07% for the given potential energy surface for temperatures in the range 300–3000 K and are the most accurately converged partition functions for a given potential energy surface for any molecule with five or more atoms. We also tabulate free energies, enthalpies, entropies, and heat capacities.
NASA Technical Reports Server (NTRS)
Simon, Donald L.
2010-01-01
Aircraft engine performance trend monitoring and gas path fault diagnostics are closely related technologies that assist operators in managing the health of their gas turbine engine assets. Trend monitoring is the process of monitoring the gradual performance change that an aircraft engine will naturally incur over time due to turbomachinery deterioration, while gas path diagnostics is the process of detecting and isolating the occurrence of any faults impacting engine flow-path performance. Today, performance trend monitoring and gas path fault diagnostic functions are performed by a combination of on-board and off-board strategies. On-board engine control computers contain logic that monitors for anomalous engine operation in real-time. Off-board ground stations are used to conduct fleet-wide engine trend monitoring and fault diagnostics based on data collected from each engine each flight. Continuing advances in avionics are enabling the migration of portions of the ground-based functionality on-board, giving rise to more sophisticated on-board engine health management capabilities. This paper reviews the conventional engine performance trend monitoring and gas path fault diagnostic architecture commonly applied today, and presents a proposed enhanced on-board architecture for future applications. The enhanced architecture gains real-time access to an expanded quantity of engine parameters, and provides advanced on-board model-based estimation capabilities. The benefits of the enhanced architecture include the real-time continuous monitoring of engine health, the early diagnosis of fault conditions, and the estimation of unmeasured engine performance parameters. A future vision to advance the enhanced architecture is also presented and discussed
NASA Astrophysics Data System (ADS)
Cruz, Anthony; López, Gustavo E.
2014-04-01
By using path integral Monte Carlo simulations coupled to Replica Exchange algorithms, various phases of (p-H2)7 physically adsorbed on a model graphite surface were identified at low temperatures. At T=0.5 K, the expected superfluid phase was observed for flat and slightly corrugated surfaces. At intermediate and high corrugations, a "supersolid" phase in C7/16 registry and a solid phase in C1/3 registry were observed, respectively. At higher temperatures, the superfluid is converted to a fluid and the "supersolid" to a solid.
Kessler, Jan; Elgabarty, Hossam; Spura, Thomas; Karhan, Kristof; Partovi-Azar, Pouya; Hassanali, Ali A; Kühne, Thomas D
2015-08-06
The structure and dynamics of the water/vapor interface is revisited by means of path-integral and second-generation Car-Parrinello ab initio molecular dynamics simulations in conjunction with an instantaneous surface definition [Willard, A. P.; Chandler, D. J. Phys. Chem. B 2010, 114, 1954]. In agreement with previous studies, we find that one of the OH bonds of the water molecules in the topmost layer is pointing out of the water into the vapor phase, while the orientation of the underlying layer is reversed. Therebetween, an additional water layer is detected, where the molecules are aligned parallel to the instantaneous water surface.
NASA Astrophysics Data System (ADS)
Takayanagi, Toshiyuki; Shiga, Motoyuki
2002-08-01
The structures and vibrational frequencies of Cl 2-helium clusters have been studied using the path integral molecular dynamics method combined with the discrete-variable-representation approach. It is found that the Cl 2-helium clusters form clear shell structures comprised of rings around the Cl 2 bond. The vibrational frequencies calculated show a monotonically increasing red shift with an increase in cluster size. It can be concluded that the first solvation shell and its density around T-shaped configurations play the most important role in the observed frequency shifts.
NASA Astrophysics Data System (ADS)
Takayanagi, Toshiyuki; Shiga, Motoyuki
2003-04-01
The photodissociation dynamics of Cl 2 embedded in helium clusters is studied by numerical simulation with an emphasis on the effect of quantum character of helium motions. The simulation is based on the hybrid model in which Cl-Cl internuclear dynamics is treated in a wavepacket technique, while the helium motions are described by a path integral centroid molecular dynamics approach. It is found that the cage effect largely decreases when the helium motion is treated quantum mechanically. The mechanism is affected not only by the zero-point vibration in the helium solvation structure, but also by the quantum dynamics of helium.
NASA Astrophysics Data System (ADS)
Sugawara, Shuichi; Yoshikawa, Takehiro; Takayanagi, Toshiyuki; Tachikawa, Masanori
2011-01-01
The structural rearrangement process for the HCl(H2O)4 cluster has been studied by path-integral molecular dynamics simulations, where 'on-the-fly' calculation of the potential energy surface is done with the PM3-MAIS semiempirical level. The mechanisms of the rearrangement were analyzed using appropriate collective coordinates as well as detailed potential energy diagrams derived from low-lying stationary points. It was found that the vibrational entropy mainly determines the stability of the cluster structure especially at high temperatures. We have also found that the acidity of HCl in the cluster correlates with the coordination number of chlorine with respect water molecules.
NASA Astrophysics Data System (ADS)
Mizumoto, Yoshihiko; Ohtsuki, Yukiyoshi
2011-01-01
Path integral molecular dynamics simulation is used to study the rotational motion of a CO molecule doped in a large para-hydrogen (p-H2) cluster. The quasi-free rotational motion of CO in a p-H2 cluster with a reduced rotational constant is derived from the imaginary-time orientational correlation functions, and is in good agreement with recent experimental observations. We attribute the reduced rotational constant to the low-viscous fluid-like behavior of the host p-H2 cluster.
NASA Astrophysics Data System (ADS)
Takayanagi, Toshiyuki; Takahashi, Kenta; Kakizaki, Akira; Shiga, Motoyuki; Tachikawa, Masanori
2009-04-01
Path-integral molecular dynamics simulations for the HCl(H 2O) 4 cluster have been performed on the ground-state potential energy surface directly obtained on-the-fly from semiempirical PM3-MAIS molecular orbital calculations. It is found that the HCl(H 2O) 4 cluster has structural rearrangement above the temperature of 300 K showing a liquid-like behavior. Quantum mechanical fluctuation of hydrogen nuclei plays a significant role in structural arrangement processes in this cluster.
Khavrutskii, Ilja V; Byrd, Richard H; Brooks, Charles L
2006-05-21
A variation of the line integral method of Elber with self-avoiding walk has been implemented using a state of the art nonlinear constrained optimization procedure. The new implementation appears to be robust in finding approximate reaction paths for small and large systems. Exact transition states and intermediates for the resulting paths can easily be pinpointed with subsequent application of the conjugate peak refinement method [S. Fischer and M. Karplus, Chem. Phys. Lett. 194, 252 (1992)] and unconstrained minimization, respectively. Unlike previous implementations utilizing a penalty function approach, the present implementation generates an exact solution of the underlying problem. Most importantly, this formulation does not require an initial guess for the path, which makes it particularly useful for studying complex molecular rearrangements. The method has been applied to conformational rearrangements of the alanine dipeptide in the gas phase and in water, and folding of the beta hairpin of protein G in water. In the latter case a procedure was developed to systematically sample the potential energy surface underlying folding and reconstruct folding pathways within the nearest-neighbor hopping approximation.
Layne, John E; Barnes, W Jon P; Duncan, Lindsey M J
2003-12-01
Fiddler crabs Uca rapax are central-place foragers, making feeding excursions of up to several meters from their burrows. This study investigates the sources of directional and distance information used by these crabs when returning to their burrows. We tested the spatial frame of reference (egocentric or exocentric), and the source of spatial information (idiothetic or allothetic) used during homing. We also tested which components of their locomotion they integrated (only voluntary, or voluntary plus reflexive). Fiddler crabs in their natural mudflat habitat were passively rotated during normal foraging behavior using experimenter-controlled disks, before they returned home. Crabs resisted passive rotations on the disk by counter-rotating when the disk turned, which was a compensatory response to unintended movement. Crabs were usually situated eccentrically on the disk, and therefore were also subjected to a translation when the disk rotated. No crab actively compensated for this translation. Crabs that fully compensated for disk rotation made no directional homing error. Crabs that did not fully compensate homed in a direction that reflected their new body orientation. In other words, if we succeeded in reorienting a crab (i.e. it undercompensated for disk rotation), its homing error was equal to the angle by which it had been reoriented, regardless of the magnitude of the optomotor compensation. Computer-modelled crabs, each equipped with a path integrator utilizing different combinations of external (allothetic) and path-related (idiothetic) input, traversed the digitized paths of the real crabs. The home vector computed by the model crab was then compared to the homing direction observed in the real crab. The model home vector that most closely matched that of the real crab was taken to comprise the path integration mechanism employed by fiddler crabs. The model that best matched the real crab gained direction and distance idiothetically (from internal
Kwon, TaeKyu; Agrawal, Kunal; Li, Yunfeng; Pizlo, Zygmunt
2015-01-01
Finding the occluding contours of objects in real 2D retinal images of natural 3D scenes is done by determining, which contour fragments are relevant, and the order in which they should be connected. We developed a model that finds the closed contour represented in the image by solving a shortest path problem that uses a log-polar representation of the image; the kind of representation known to exist in area V1 of the primate cortex. The shortest path in a log-polar representation favors the smooth, convex and closed contours in the retinal image that have the smallest number of gaps. This approach is practical because finding a globally-optimal solution to a shortest path problem is computationally easy. Our model was tested in four psychophysical experiments. In the first two experiments, the subject was presented with a fragmented convex or concave polygon target among a large number of unrelated pieces of contour (distracters). The density of these pieces of contour was uniform all over the screen to minimize spatially-local cues. The orientation of each target contour fragment was randomly perturbed by varying the levels of jitter. Subjects drew a closed contour that represented the target’s contour on a screen. The subjects’ performance was nearly perfect when the jitter-level was low. Their performance deteriorated as jitter-levels were increased. The performance of our model was very similar to our subjects’. In two subsequent experiments, the subject was asked to discriminate a briefly-presented egg-shaped object while maintaining fixation at several different positions relative to the closed contour of the shape. The subject’s discrimination performance was affected by the fixation position in much the same way as the model’s. PMID:26241462
Ivanov, Sergei D. Grant, Ian M.; Marx, Dominik
2015-09-28
With the goal of computing quantum free energy landscapes of reactive (bio)chemical systems in multi-dimensional space, we combine the metadynamics technique for sampling potential energy surfaces with the ab initio path integral approach to treating nuclear quantum motion. This unified method is applied to the double proton transfer process in the formic acid dimer (FAD), in order to study the nuclear quantum effects at finite temperatures without imposing a one-dimensional reaction coordinate or reducing the dimensionality. Importantly, the ab initio path integral metadynamics technique allows one to treat the hydrogen bonds and concomitant proton transfers in FAD strictly independently and thus provides direct access to the much discussed issue of whether the double proton transfer proceeds via a stepwise or concerted mechanism. The quantum free energy landscape we compute for this H-bonded molecular complex reveals that the two protons move in a concerted fashion from initial to product state, yet world-line analysis of the quantum correlations demonstrates that the protons are as quantum-uncorrelated at the transition state as they are when close to the equilibrium structure.
Ivanov, Sergei D; Grant, Ian M; Marx, Dominik
2015-09-28
With the goal of computing quantum free energy landscapes of reactive (bio)chemical systems in multi-dimensional space, we combine the metadynamics technique for sampling potential energy surfaces with the ab initio path integral approach to treating nuclear quantum motion. This unified method is applied to the double proton transfer process in the formic acid dimer (FAD), in order to study the nuclear quantum effects at finite temperatures without imposing a one-dimensional reaction coordinate or reducing the dimensionality. Importantly, the ab initio path integral metadynamics technique allows one to treat the hydrogen bonds and concomitant proton transfers in FAD strictly independently and thus provides direct access to the much discussed issue of whether the double proton transfer proceeds via a stepwise or concerted mechanism. The quantum free energy landscape we compute for this H-bonded molecular complex reveals that the two protons move in a concerted fashion from initial to product state, yet world-line analysis of the quantum correlations demonstrates that the protons are as quantum-uncorrelated at the transition state as they are when close to the equilibrium structure.
Webb, Michael A; Miller, Thomas F
2014-01-16
We combine path-integral Monte Carlo methods with high-quality potential energy surfaces to compute equilibrium isotope effects in a variety of systems relevant to 'clumped' isotope analysis and isotope geochemistry, including CO2, N2O, methane, and propane. Through a systematic study of heavy-atom isotope-exchange reactions, we quantify and analyze errors that arise in the widely used Urey model for predicting equilibrium constants of isotope-exchange reactions using reduced partition function ratios. These results illustrate that the Urey model relies on a nontrivial cancellation of errors that can shift the apparent equilibrium temperature by as much as 35 K for a given distribution of isotopologues. The calculations reported here provide the same level of precision as the best existing analytical instrumentation, resolving the relative enrichment of certain isotopologues to as little as 0.01‰. These findings demonstrate path-integral methods to be a rigorous and viable alternative to more approximate methods for heavy-atom geochemical applications.
Mielke, Steven L; Truhlar, Donald G
2009-04-23
We present two enhancements to our methods for calculating vibrational-rotational free energies by Feynman path integrals, namely, a sequential sectioning scheme for efficiently generating random free-particle paths and a stratified sampling scheme that uses the energy of the path centroids. These improved methods are used with three interaction potentials to calculate equilibrium constants for the fractionation behavior of Cl(-) hydration in the presence of a gas-phase mixture of H(2)O, D(2)O, and HDO. Ion cyclotron resonance experiments indicate that the equilibrium constant, K(eq), for the reaction Cl(H(2)O)(-) + D(2)O right harpoon over left harpoon Cl(D(2)O)(-) + H(2)O is 0.76, whereas the three theoretical predictions are 0.946, 0.979, and 1.20. Similarly, the experimental K(eq) for the Cl(H(2)O)(-) + HDO right harpoon over left harpoon Cl(HDO)(-) + H(2)O reaction is 0.64 as compared to theoretical values of 0.972, 0.998, and 1.10. Although Cl(H(2)O)(-) has a large degree of anharmonicity, K(eq) values calculated with the harmonic oscillator rigid rotator (HORR) approximation agree with the accurate treatment to within better than 2% in all cases. Results of a variety of electronic structure calculations, including coupled cluster and multireference configuration interaction calculations, with either the HORR approximation or with anharmonicity estimated via second-order vibrational perturbation theory, all agree well with the equilibrium constants obtained from the analytical surfaces.
NASA Technical Reports Server (NTRS)
Campbell, R. H.; Kolstad, R. B.; Holle, D. F.; Miller, T. J.; Krause, P.; Horton, K.; Macke, T.
1983-01-01
Path Pascal is high-level experimental programming language based on PASCAL, which incorporates extensions for systems and real-time programming. Pascal is extended to treat real-time concurrent systems.
NASA Technical Reports Server (NTRS)
Singh, U. N.; Yu, J.; Petros, M.; Refaat, T. F.; Remus, R.; Fay, J.; Reithmaier, K.
2014-01-01
NASA LaRC is developing and integrating a double-Pulsed 2-micron direct detection IPDA lidar for CO2 column measurement from an airborne platform. The presentation will describe the development of the 2-micrometers IPDA lidar system and present the airborne measurement of column CO2 and will compare to in-situ measurement for various ground target of different reflectivity.
ERIC Educational Resources Information Center
Hasio, Cindy; Crane, Tommy J.
2014-01-01
Interior design is seldom integrated within the general art education curriculum because the subject matter is generally segregated as a commercial art. However, the importance of interior design concepts of sustainability in art education can really help a student understand the scale and proportion of space and mass, and how sustainability is…
Burton, Bethany L.; Ball, Lyndsay B.; Stanton, Gregory P.; Hobza, Christopher M.
2009-01-01
In May 2006, the U.S. Geological Survey, in cooperation with the U.S. Army Corps of Engineers, conducted surface and borehole geophysical surveys at the former Tyson Valley Powder Farm near Eureka, Mo., to identify preferential pathways for potential contaminant transport along the bedrock surface and into dissolution-enhanced fractures. The Tyson Valley Powder Farm was formerly used as a munitions storage and disposal facility in the 1940s and 1950s, and the site at which the surveys were performed was a disposal area for munitions and waste solvents such as trichloroethylene and dichloroethylene. Direct-current resistivity and seismic refraction data were acquired on the surface; gamma, electromagnetic induction, and full waveform sonic logs were acquired in accessible boreholes. Through the combined interpretation of the seismic refraction tomographic and resistivity inversion results and borehole logs, inconsistencies in the bedrock surface were identified that may provide horizontal preferential flow paths for dense nonaqueous phase liquid contaminants. These results, interpreted and displayed in georeferenced three-dimensional space, should help to establish more effective monitoring and remediation strategies.
NASA Astrophysics Data System (ADS)
Yan, Yangqian; Blume, D.
2016-05-01
The unitary equal-mass Fermi gas with zero-range interactions constitutes a paradigmatic model system that is relevant to atomic, condensed matter, nuclear, particle, and astro physics. This work determines the fourth-order virial coefficient b4 of such a strongly-interacting Fermi gas using a customized ab inito path integral Monte Carlo (PIMC) algorithm. In contrast to earlier theoretical results, which disagreed on the sign and magnitude of b4, our b4 agrees with the experimentally determined value, thereby resolving an ongoing literature debate. Utilizing a trap regulator, our PIMC approach determines the fourth-order virial coefficient by directly sampling the partition function. An on-the-fly anti-symmetrization avoids the Thomas collapse and, combined with the use of the exact two-body zero-range propagator, establishes an efficient general means to treat small Fermi systems with zero-range interactions. We gratefully acknowledge support by the NSF.
NASA Astrophysics Data System (ADS)
Yan, Yangqian; Blume, D.
2016-06-01
The unitary equal-mass Fermi gas with zero-range interactions constitutes a paradigmatic model system that is relevant to atomic, condensed matter, nuclear, particle, and astrophysics. This work determines the fourth-order virial coefficient b4 of such a strongly interacting Fermi gas using a customized ab initio path-integral Monte Carlo (PIMC) algorithm. In contrast to earlier theoretical results, which disagreed on the sign and magnitude of b4 , our b4 agrees within error bars with the experimentally determined value, thereby resolving an ongoing literature debate. Utilizing a trap regulator, our PIMC approach determines the fourth-order virial coefficient by directly sampling the partition function. An on-the-fly antisymmetrization avoids the Thomas collapse and, combined with the use of the exact two-body zero-range propagator, establishes an efficient general means to treat small Fermi systems with zero-range interactions.
NASA Astrophysics Data System (ADS)
Motegi, Haruki; Kakizaki, Akira; Takayanagi, Toshiyuki; Taketsugu, Yuriko; Taketsugu, Tetsuya; Shiga, Motoyuki
2008-12-01
Path-integral molecular dynamics simulations have been performed to understand the quantum helium solvation structures in the He nBeO cluster up to n = 100. Our simulations show that one helium atom is strongly bound to BeO to form HeBeO and that the first solvation shell around the HeBeO complex includes roughly 12-14 helium atoms. The second solvation structure was also observed for n > 20. Both the first and second solvation shells show an anisotropic behavior but the anisotropy for the second solvation shell was found to be much weaker than that for the first solvation shell, as expected. The present simulations suggest that the HeBeO complex may be formed in large helium clusters.
NASA Astrophysics Data System (ADS)
Yoshikawa, Takehiro; Motegi, Haruki; Kakizaki, Akira; Takayanagi, Toshiyuki; Shiga, Motoyuki; Tachikawa, Masanori
2009-11-01
Path-integral molecular dynamics simulations for the hydrogen-bonded glycine·(H 2O) n ( n = 1-7) clusters have been carried out using an on-the-fly direct dynamics technique at the semi-empirical PM6 level of theory. In the case of smaller clusters with n = 1-3, the simulations show that the cluster structure takes exclusively the hydrogen-bonded complex between a canonical neutral glycine and a water cluster moiety. In contrast, it was found that proton-exchange processes effectively occur between the COOH carboxylic group and water cluster moiety for n = 4-6 clusters although the overall structures are the complex between a neutral glycine and water clusters. In the case of the n = 7 cluster, glycine preferentially takes a zwitterionic form having NH3+ and COO - functional groups.
NASA Astrophysics Data System (ADS)
Hayashi, Aiko; Shiga, Motoyuki; Tachikawa, Masanori
2006-11-01
In order to investigate the H /D isotope effect on a dihydrogen bonded cation system, we have studied NH4+⋯BeH2 and its isotopomers by ab initio path integral molecular dynamics. It is found that the dihydrogen bond can be exchanged by NH4+ rotation. The deuterated isotopomer (ND4+⋯BeD2; DD) can exchange the dihydrogen bond more easily than other isotopomers such as (NH4+⋯BeH2; HH). This unusual isotope effect is ascribed to the "quantum localization" which occurs when the effective energy barrier for the rotational mode becomes higher by the zero point energy of other modes. We also found that the binding energy of dihydrogen bonds for DD species is the smallest among the isotopomers.
NASA Astrophysics Data System (ADS)
Oh, Ki-Dong; Deymier, P. A.
2004-04-01
We have used the restricted path-integral molecular dynamics method to study the correlated electronic structure of a half-filled expanded three-dimensional hydrogenoid body-centered cubic lattice at finite temperatures. Starting from a paramagnetic metallic state with electron gas character, we find that bound electrons form upon expansion of the lattice. The bound electrons are spatially localized with their center for the motion of gyration located on ionic positions. The region of coexistence of bound and unbound states in the temperature-density plane is reminiscent of that associated with a first-order transition. At constant temperature, the number of bound electrons increases monotonously with decreasing density. The width of the region of coexistence narrows with increasing temperature.
Zimmermann, Tomáš; Vaníček, Jiří
2010-11-01
Recent experiments have confirmed the importance of nuclear quantum effects even in large biomolecules at physiological temperature. Here we describe how the path integral formalism can be used to describe rigorously the nuclear quantum effects on equilibrium and kinetic properties of molecules. Specifically, we explain how path integrals can be employed to evaluate the equilibrium (EIE) and kinetic (KIE) isotope effects, and the temperature dependence of the rate constant. The methodology is applied to the [1,5] sigmatropic hydrogen shift in pentadiene. Both the KIE and the temperature dependence of the rate constant confirm the importance of tunneling and other nuclear quantum effects as well as of the anharmonicity of the potential energy surface. Moreover, previous results on the KIE were improved by using a combination of a high level electronic structure calculation within the harmonic approximation with a path integral anharmonicity correction using a lower level method.
NASA Astrophysics Data System (ADS)
Caspani, Lucia; Reimer, Christian; Kues, Michael; Roztocki, Piotr; Clerici, Matteo; Wetzel, Benjamin; Jestin, Yoann; Ferrera, Marcello; Peccianti, Marco; Pasquazi, Alessia; Razzari, Luca; Little, Brent E.; Chu, Sai T.; Moss, David J.; Morandotti, Roberto
2016-06-01
Recent developments in quantum photonics have initiated the process of bringing photonic-quantumbased systems out-of-the-lab and into real-world applications. As an example, devices to enable the exchange of a cryptographic key secured by the laws of quantum mechanics are already commercially available. In order to further boost this process, the next step is to transfer the results achieved by means of bulky and expensive setups into miniaturized and affordable devices. Integrated quantum photonics is exactly addressing this issue. In this paper, we briefly review the most recent advancements in the generation of quantum states of light on-chip. In particular, we focus on optical microcavities, as they can offer a solution to the problem of low efficiency that is characteristic of the materials typically used in integrated platforms. In addition, we show that specifically designed microcavities can also offer further advantages, such as compatibility with telecom standards (for exploiting existing fibre networks) and quantum memories (necessary to extend the communication distance), as well as giving a longitudinal multimode character for larger information transfer and processing. This last property (i.e., the increased dimensionality of the photon quantum state) is achieved through the ability to generate multiple photon pairs on a frequency comb, corresponding to the microcavity resonances. Further achievements include the possibility of fully exploiting the polarization degree of freedom, even for integrated devices. These results pave the way for the generation of integrated quantum frequency combs that, in turn, may find important applications toward the realization of a compact quantum-computing platform.
NASA Technical Reports Server (NTRS)
Stonesifer, R. B.; Atluri, S. N.
1982-01-01
The development of valid creep fracture criteria is considered. Two path-independent integral parameters which show some degree of promise are the C* and (Delta T)sub c integrals. The mathematical aspects of these parameters are reviewed by deriving generalized vector forms of the parameters using conservation laws which are valid for arbitrary, three dimensional, cracked bodies with crack surface tractions (or applied displacements), body forces, inertial effects, and large deformations. Two principal conclusions are that (Delta T)sub c has an energy rate interpretation whereas C* does not. The development and application of fracture criteria often involves the solution of boundary/initial value problems associated with deformation and stresses. The finite element method is used for this purpose. An efficient, small displacement, infinitesimal strain, displacement based finite element model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations. A mesh shifting/remeshing procedure is used for simulating crack growth. The model is implemented with the quartz-point node technique and also with specially developed, conforming, crack-tip singularity elements which provide for the r to the n-(1+n) power strain singularity associated with the HRR crack-tip field. Comparisons are made with a variety of analytical solutions and alternate numerical solutions for a number of problems.
Palmintier, Bryan; Broderick, Robert; Mather, Barry; Coddington, Michael; Baker, Kyri; Ding, Fei; Reno, Matthew; Lave, Matthew; Bharatkumar, Ashwini
2016-05-01
This report analyzes distribution-integration challenges, solutions, and research needs in the context of distributed generation from PV (DGPV) deployment to date and the much higher levels of deployment expected with achievement of the U.S. Department of Energy's SunShot targets. Recent analyses have improved estimates of the DGPV hosting capacities of distribution systems. This report uses these results to statistically estimate the minimum DGPV hosting capacity for the contiguous United States using traditional inverters of approximately 170 GW without distribution system modifications. This hosting capacity roughly doubles if advanced inverters are used to manage local voltage and additional minor, low-cost changes could further increase these levels substantially. Key to achieving these deployment levels at minimum cost is siting DGPV based on local hosting capacities, suggesting opportunities for regulatory, incentive, and interconnection innovation. Already, pre-computed hosting capacity is beginning to expedite DGPV interconnection requests and installations in select regions; however, realizing SunShot-scale deployment will require further improvements to DGPV interconnection processes, standards and codes, and compensation mechanisms so they embrace the contributions of DGPV to system-wide operations. SunShot-scale DGPV deployment will also require unprecedented coordination of the distribution and transmission systems. This includes harnessing DGPV's ability to relieve congestion and reduce system losses by generating closer to loads; minimizing system operating costs and reserve deployments through improved DGPV visibility; developing communication and control architectures that incorporate DGPV into system operations; providing frequency response, transient stability, and synthesized inertia with DGPV in the event of large-scale system disturbances; and potentially managing reactive power requirements due to large-scale deployment of advanced inverter
NASA Technical Reports Server (NTRS)
Berman, A. L.
1977-01-01
Observations of Viking differenced S-band/X-band (S-X) range are shown to correlate strongly with Viking Doppler noise. A ratio of proportionality between downlink S-band plasma-induced range error and two-way Doppler noise is calculated. A new parameter (similar to the parameter epsilon which defines the ratio of local electron density fluctuations to mean electron density) is defined as a function of observed data sample interval (Tau) where the time-scale of the observations is 15 Tau. This parameter is interpreted to yield the ratio of net observed phase (or electron density) fluctuations to integrated electron density (in RMS meters/meter). Using this parameter and the thin phase-changing screen approximation, a value for the scale size L is calculated. To be consistent with Doppler noise observations, it is seen necessary for L to be proportional to closest approach distance a, and a strong function of the observed data sample interval, and hence the time-scale of the observations.
NASA Astrophysics Data System (ADS)
Rehmat, Abeera Parvaiz
As we progress into the 21st century, higher-order thinking skills and achievement in science and math are essential to meet the educational requirement of STEM careers. Educators need to think of innovative ways to engage and prepare students for current and future challenges while cultivating an interest among students in STEM disciplines. An instructional pedagogy that can capture students' attention, support interdisciplinary STEM practices, and foster higher-order thinking skills is problem-based learning. Problem-based learning embedded in the social constructivist view of teaching and learning (Savery & Duffy, 1995) promotes self-regulated learning that is enhanced through exploration, cooperative social activity, and discourse (Fosnot, 1996). This quasi-experimental mixed methods study was conducted with 98 fourth grade students. The study utilized STEM content assessments, a standardized critical thinking test, STEM attitude survey, PBL questionnaire, and field notes from classroom observations to investigate the impact of problem-based learning on students' content knowledge, critical thinking, and their attitude towards STEM. Subsequently, it explored students' experiences of STEM integration in a PBL environment. The quantitative results revealed a significant difference between groups in regards to their content knowledge, critical thinking skills, and STEM attitude. From the qualitative results, three themes emerged: learning approaches, increased interaction, and design and engineering implementation. From the overall data set, students described the PBL environment to be highly interactive that prompted them to employ multiple approaches, including design and engineering to solve the problem.
Kowalczyk, Piotr; Gauden, Piotr A; Terzyk, Artur P; Bhatia, Suresh K
2007-03-27
Hydrogen in slit-like carbon nanopores at 77 K represents a quantum fluid in strong confinement. We have used path-integral grand canonical Monte Carlo and classical grand canonical Monte Carlo simulations for the investigation of the "quantumness" of hydrogen at 77 K adsorbed in slit-like carbon nanopores up to 1 MPa. We find that classical simulations overpredict the hydrogen uptake in carbon nanopores due to neglect of the quantum delocalization. Such disagreement of both simulation methods depends on the slit-like carbon pore size. However, the differences between the final uptakes of hydrogen computed from both classical and quantum simulations are not large due to a similar effective size of quantum/classical hydrogen molecules in carbon nanospaces. For both types of molecular simulations, the volumetric density of stored energy in optimal carbon nanopores exceeds 6.4 MJ dm(-3) (i.e., 45 kg m(-3); Department of Energy target for 2010). In contrast to the hydrogen adsorption isotherms, we found a large reduction of isosteric enthalpy of adsorption computed from the quantum Feynman's path-integral simulations in comparison to the classical values at 77 K and pressures up to 1 MPa. Depression of the quantum isosteric enthalpy of adsorption depends on the slit-like carbon pore size. For the narrow pores (pore width H in [0.59-0.7] nm), the reduction of the quantum isosteric enthalpy of adsorption at zero coverage is around 50% in comparison to the classical one. We observed new phenomena called, by us, the quantum confinement-inducing polymer shrinking. In carbon nanospaces, the quantum cyclic polymers shrink, in comparison to its bulk-phase counterpart, due to a strong confinement effect. At considered storage conditions, this complex phenomenon depends on the size of the slit-like carbon nanopore and the density of hydrogen volumetric energy. For the smallest nanopores and a low density of hydrogen volumetric energy, the reduction of the polymer effective size
Robbins, Steven B; Oh, In-Sue; Le, Huy; Button, Christopher
2009-09-01
Using both organizational and educational perspectives, the authors proposed and tested theoretical models on the mediating roles that psychosocial factors (PSFs; motivational, emotional, and social control factors) play between college interventions (academic skill, self-management, socialization, and First-Year-Experience interventions) and college outcomes (academic performance and retention). They first determined through meta-analysis of 404 data points the effects of college interventions on college outcomes and on PSFs. These meta-analytic findings were then combined with results from S. B. Robbins et al.'s (2004) meta-analysis to test the proposed models. Integrated meta-analytic path analyses showed the direct and indirect effects (via PSFs) of intervention strategies on both performance and retention outcomes. The authors highlight the importance of both academic skill and self-management-based interventions; they also note the salience of motivational and emotional control mediators across both performance and retention outcomes. Implications from organizational and educational perspectives, limitations, and future directions are addressed.
McBride, Carl; Aragones, Juan L; Noya, Eva G; Vega, Carlos
2012-11-21
The melting point of ice I(h), as well as the temperature of maximum density (TMD) in the liquid phase, has been computed using the path integral Monte Carlo method. Two new models are introduced, TIP4PQ_D2O and TIP4PQ_T2O, which are specifically designed to study D(2)O and T(2)O respectively. We have also used these models to study the "competing quantum effects" proposal of Habershon, Markland and Manolopoulos; the TIP4PQ/2005, TIP4PQ/2005 (D(2)O) and TIP4PQ/2005 (T(2)O) models are able to study the isotopic substitution of hydrogen for deuterium or tritium whilst constraining the geometry, while the TIP4PQ_D2O and TIP4PQ_T2O models, where the O-H bond lengths are progressively shortened, permit the study of the influence of geometry (and thus dipole moment) on the isotopic effects. For TIP4PQ_D2O-TIP4PQ/2005 we found a melting point shift of 4.9 K (experimentally the value is 3.68 K) and a TMD shift of 6 K (experimentally 7.2 K). For TIP4PQ_T2O-TIP4PQ/2005 we found a melting point shift of 5.2 K (experimentally the value is 4.49 K) and a TMD shift of 7 K (experimentally 9.4 K).
NASA Astrophysics Data System (ADS)
Tiihonen, Juha; Kylänpää, Ilkka; Rantala, Tapio T.
2016-09-01
The nonlinear optical properties of matter have a broad relevance and many methods have been invented to compute them from first principles. However, the effects of electronic correlation, finite temperature, and breakdown of the Born-Oppenheimer approximation have turned out to be challenging and tedious to model. Here we propose a straightforward approach and derive general field-free polarizability and hyperpolarizability estimators for the path-integral Monte Carlo method. The estimators are applied to small atoms, ions, and molecules with one or two electrons. With the adiabatic, i.e., Born-Oppenheimer, approximation we obtain accurate tensorial ground state polarizabilities, while the nonadiabatic simulation adds in considerable rovibrational effects and thermal coupling. In both cases, the 0 K, or ground-state, limit is in excellent agreement with the literature. Furthermore, we report here the internal dipole moment of PsH molecule, the temperature dependence of the polarizabilities of H-, and the average dipole polarizabilities and the ground-state hyperpolarizabilities of HeH+ and H 3 + .
Sasaki, Akira; Kojo, Masashi; Hirose, Kikuji; Goto, Hidekazu
2011-11-02
The path-integral renormalization group and direct energy minimization method of practical first-principles electronic structure calculations for multi-body systems within the framework of the real-space finite-difference scheme are introduced. These two methods can handle higher dimensional systems with consideration of the correlation effect. Furthermore, they can be easily extended to the multicomponent quantum systems which contain more than two kinds of quantum particles. The key to the present methods is employing linear combinations of nonorthogonal Slater determinants (SDs) as multi-body wavefunctions. As one of the noticeable results, the same accuracy as the variational Monte Carlo method is achieved with a few SDs. This enables us to study the entire ground state consisting of electrons and nuclei without the need to use the Born-Oppenheimer approximation. Recent activities on methodological developments aiming towards practical calculations such as the implementation of auxiliary field for Coulombic interaction, the treatment of the kinetic operator in imaginary-time evolutions, the time-saving double-grid technique for bare-Coulomb atomic potentials and the optimization scheme for minimizing the total-energy functional are also introduced. As test examples, the total energy of the hydrogen molecule, the atomic configuration of the methylene and the electronic structures of two-dimensional quantum dots are calculated, and the accuracy, availability and possibility of the present methods are demonstrated.
NASA Astrophysics Data System (ADS)
Habershon, Scott
2013-09-01
We introduce a new approach for calculating quantum time-correlation functions and time-dependent expectation values in many-body thermal systems; both electronically adiabatic and non-adiabatic cases can be treated. Our approach uses a path integral simulation to sample an initial thermal density matrix; subsequent evolution of this density matrix is equivalent to solution of the time-dependent Schrödinger equation, which we perform using a linear expansion of Gaussian wavepacket basis functions which evolve according to simple classical-like trajectories. Overall, this methodology represents a formally exact approach for calculating time-dependent quantum properties; by introducing approximations into both the imaginary-time and real-time propagations, this approach can be adapted for complex many-particle systems interacting through arbitrary potentials. We demonstrate this method for the spin Boson model, where we find good agreement with numerically exact calculations. We also discuss future directions of improvement for our approach with a view to improving accuracy and efficiency.
Kawashima, Yukio; Suzuki, Kimichi; Tachikawa, Masanori
2013-06-20
Small hydrated fluoride ion complexes, F(-)(H2O)n (n = 1-3), have been studied by ab initio hybrid Monte Carlo (HMC) and ab initio path integral hybrid Monte Carlo (PIHMC) simulations. Because of the quantum effect, our simulation shows that the average hydrogen-bonded F(-)···HO distance in the quantum F(-)(H2O) is shorter than that in the classical one, while the relation inverts at the three water molecular F(-)(H2O)3 cluster. In the case of F(-)(H2O)3, we have found that the nuclear quantum effect enhances the formation of hydrogen bonds between two water molecules. In F(-)(H2O)2 and F(-)(H2O)3, the nuclear quantum effect on two different kinds of hydrogen bonds, F(-)-water and water-water hydrogen bonds, competes against each other. In F(-)(H2O)3, thus, the nuclear quantum effect on the water-water hydrogen bond leads to the elongation of hydrogen-bonded F(-)···HO distance, which we suggest this as the possible origin of the structural inversion from F(-)(H2O) to F(-)(H2O)3.
NASA Technical Reports Server (NTRS)
Haggerty, Julie; McDonough, Frank; Black, Jennifer; Landott, Scott; Wolff, Cory; Mueller, Steven; Minnis, Patrick; Smith, William, Jr.
2008-01-01
Operational products used by the U.S. Federal Aviation Administration to alert pilots of hazardous icing provide nowcast and short-term forecast estimates of the potential for the presence of supercooled liquid water and supercooled large droplets. The Current Icing Product (CIP) system employs basic satellite-derived information, including a cloud mask and cloud top temperature estimates, together with multiple other data sources to produce a gridded, three-dimensional, hourly depiction of icing probability and severity. Advanced satellite-derived cloud products developed at the NASA Langley Research Center (LaRC) provide a more detailed description of cloud properties (primarily at cloud top) compared to the basic satellite-derived information used currently in CIP. Cloud hydrometeor phase, liquid water path, cloud effective temperature, and cloud top height as estimated by the LaRC algorithms are into the CIP fuzzy logic scheme and a confidence value is determined. Examples of CIP products before and after the integration of the LaRC satellite-derived products will be presented at the conference.
NASA Technical Reports Server (NTRS)
Refaat, Tamer F.; Singh, Upendra N.; Petros, Mulugeta; Remus, Ruben; Yu, Jirong
2015-01-01
Double-pulsed 2-micron integrated path differential absorption (IPDA) lidar is well suited for atmospheric CO2 remote sensing. The IPDA lidar technique relies on wavelength differentiation between strong and weak absorbing features of the gas normalized to the transmitted energy. In the double-pulse case, each shot of the transmitter produces two successive laser pulses separated by a short interval. Calibration of the transmitted pulse energies is required for accurate CO2 measurement. Design and calibration of a 2-micron double-pulse laser energy monitor is presented. The design is based on an InGaAs pin quantum detector. A high-speed photo-electromagnetic quantum detector was used for laser-pulse profile verification. Both quantum detectors were calibrated using a reference pyroelectric thermal detector. Calibration included comparing the three detection technologies in the single-pulsed mode, then comparing the quantum detectors in the double-pulsed mode. In addition, a self-calibration feature of the 2-micron IPDA lidar is presented. This feature allows one to monitor the transmitted laser energy, through residual scattering, with a single detection channel. This reduces the CO2 measurement uncertainty. IPDA lidar ground validation for CO2 measurement is presented for both calibrated energy monitor and self-calibration options. The calibrated energy monitor resulted in a lower CO2 measurement bias, while self-calibration resulted in a better CO2 temporal profiling when compared to the in situ sensor.
Poulsen, Jens Aage; Nyman, Gunnar; Rossky, Peter J
2006-11-01
The Feynman-Kleinert Linearized Path Integral (FK-LPI) representation of quantum correlation functions is extended in applications and algorithms. Diffusion including quantum effects for a flexible simple point charge model of liquid water is explored, including new tests of internal consistency. An ab initio quantum correction factor (QCF) is also obtained to correct the far-infrared spectrum of water. After correction, a spectrum based on a classical simulation is in good agreement with the experiment. The FK-LPI QCF is shown to be superior to the so-called harmonic QCF. New computational algorithms are introduced so that the quantum Boltzmann Wigner phase-space density, the central object in the implementation, can be obtained for arbitrary potentials. One scheme requires only that the standard classical force routine be replaced when turning from one molecular problem to another. The new algorithms are applied to the calculation of the Van Hove spectrum of liquid He(4) at 27 K. The spectrum moments are in very good agreement with the experiment. These observations indicate that the FK-LPI approach can be broadly effective for molecular problems involving the dynamics of light nuclei.
NASA Astrophysics Data System (ADS)
Turner, Roderick David
1990-10-01
An all-optical fiber, single-ended, polarimetric sensor system has been developed and characterized for applications in structural strain measurement, particularly in the aerospace field. Laser diode optical sources were operated at multiple wavelengths to achieve interferometric quadrature, and hence provide a linear sensor strain response. System behavior for path-integral strain measurements under DC conditions was determined for two sensors surface-adhered to aluminum cantilever beams. Linear strain responses were obtained which agreed well with theoretical sensitivities. The strain sensitivity of the polarimetric sensor at temperatures from 25 to 60 C was also found to be consistent with theory. One sensor was tested up to the 14-Hz second mode of beam vibration as a novel point-slope measuring device. The sensor responded linearly to changes in the relative orientation of its endpoints, as predicted by theory. Excellent angular tracking was demonstrated. The experimental observations are interpreted in terms of a comprehensive theoretical discussion of the polarimetric sensor's behavior, taking into account the effects of strain, temperature, and wavelength. A detailed analysis of the limitations of the sensor system is included, and recommendations are made as to the optimum practical implementation of this sensor for real applications.
NASA Astrophysics Data System (ADS)
Turner, Roderick David
1990-10-01
Recent applications for in-situ structural behavior monitoring include robotic and satellite shape sensing. An all optical fiber polarimetric sensor system was developed and characterized for applications in structural strain measurement. Laser diode optical sources were operated at multiple wavelengths to achieve interferometric quadrature, and hence provide a linear sensor strain response. The system represents the first all-fiber, dual wavelength, single-ended polarimetric sensor. System behavior for path-integral strain measurements under DC conditions was determined for two sensors of length 18.4 and 102 cm, surface adhered to aluminum cantilever beams. The longer sensor was tested under AC conditions (up to 14 Hz second mode of beam vibration) as a novel direction of pointing or point slope measurement device. The sensor responded linearly to changes in the relative orientation of its endpoints, as predicted by theory. Excellent angular tracking to +/-1 deg of orientation change, with a resolution of less than or equal 0.02 deg, was demonstrated. A comprehensive theoretical discussion of the polarimetric sensor's behavior is presented, taking into account the effects of strain, temperature and wavelength. A detailed analysis of the limitations of the sensor system is included, and recommendations are made as to the optimum practical implementation of the sensor for real applications.
NASA Astrophysics Data System (ADS)
Ehret, G.; Fix, A.; Amediek, A.; Quatrevalet, M.
2015-12-01
The Integrated Path Differential Absorption Lidar (IPDA) technique is regarded as a suitable means for the measurement of methane and carbon dioxide columns from satellite or aircraft platforms with unprecedented accuracy. Currently, the German-French methane mission MERLIN (Methan Remote Lidar Mission) is prepared. At the same time CHARM-F, an aircraft installed system has been developed at DLR as an airborne demonstrator for a spaceborne greenhouse gas mission. Both use e.g. optical parametric oscillators (OPOs) in a double-pulse mode as the transmitter. Of particular importance for both instruments are the sub-modules required for the frequency stabilization of the transmitter wavelength and, since the IPDA technique, in contrast to DIAL, requires the exact knowledge of the energy ratio of outgoing on-line. The coherence of the lidar transmitter gives rise to speckle effects which have to be considered for the monitoring of the energy ratio of outgoing on- and off-line pulses. For the frequency reference of CHARM-F, a very successful stabilization scheme has been developed which will also serve as the reference for MERLIN. In Spring 2015, CHARM-F was flown aboard the German HALO aircraft for the first time which enables a detailed view on the performance of both the energy calibration and frequency reference subsystems under real flight conditions. As an initial quality check we will compared the airborne results to previous lab measurements which have been performed under stable environmental conditions.
NASA Astrophysics Data System (ADS)
Calvo, F.
2017-01-01
The size-dependent submersion of sodium clusters into helium and para-hydrogen droplets has been computationally investigated using continuum models and path-integral molecular dynamics (PIMD) simulations. All-atom explicit potential energy surfaces combining a semiempirical many-body model for the alkali-metal subpart and a pairwise additive repulsion-dispersion contribution for the solvent-alkali-metal interactions parametrized on quantum chemical calculations were employed for the simulations. Direct evidence for the submersion process was found by placing a sufficiently large sodium cluster, NaSUB>55, initially at the surface of a He4300 droplet, whereas NaSUB>13 spontaneously migrates to the surface when initially placed at the center of this droplet. Under the normal fluid conditions probed by our approach, submersion in larger helium droplets appears thermally activated but the potential of mean force harvested from out-of-equilibrium PIMD trajectories confirms that the submersion transition occurs near the size of 20 atoms, in agreement with earlier investigations. In the case of para-hydrogen media, temperature and the crystalline nature of the cryogenic host were both found to play significant roles: while a single sodium atom migrates to the surface of liquid p -H2 clusters, it remains stuck inside at 2 K. Similarly, a NaSUB>13 cluster remains at the surface in a cold p -H2 cluster but becomes readily submerged at 16 K. Our results also indicate that submersion is disfavored in smaller droplets of the cryogenic medium.
NASA Astrophysics Data System (ADS)
Wang, Qi; Suzuki, Kimichi; Nagashima, Umpei; Tachikawa, Masanori; Yan, Shiwei
2013-06-01
The nuclear quantum effect, which plays important roles on ionic hydrogen bonded structures of Cl-(H2O)n (n = 1-4) clusters, was explored by carrying out path integral molecular dynamic simulations. An outer shell coordinate rl(Cl⋯O) is selected to display the rearrangement of single and multi hydration shell cluster structures. By incorporating the nuclear quantum effect, it is shown that the probability for single shell structures is decreased while the probability for multi shell structures is increased. On the other hand, the correlations between changing of bonded H∗ atom to Cl- (defined as δ) and other cluster vibration coordinates are studied. We have found that δ strongly correlates with proton transfer motion while it has little correlation with ion-water stretching motion. Contrary to θ(H-O-H∗) coordinate, the correlations between δ and other coordinates are decreased by inclusion of nuclear quantum effect. The results indicate that the water-water hydrogen bond interactions are encouraged by quantum simulations.
NASA Astrophysics Data System (ADS)
Saito, Hiroaki; Nagao, Hidemi; Nishikawa, Kiyoshi; Kinugawa, Kenichi
2003-07-01
The single-particle and collective dynamics of hydrogen/deuterium molecules in solid hcp para-hydrogen (p-H2) and ortho-deuterium (o-D2) has been investigated by using the path integral centroid molecular dynamics (CMD) simulations at zero-pressure and 5.4 and 5.0 K, respectively. For this purpose, we have newly unified the standard CMD method with the Parrinello-Rahman-Nosé-Hoover-chain-type isothermal-isobaric technique. The phonon density of states have been obtained and the dynamic structure factors have been calculated to observe the phonon dispersion relations of both crystals. For solid p-H2, the high energy edge of the phonon energies of solid p-H2 is >13 meV, and the calculated phonon energies are significantly higher than those observed in Nielsen's previous neutron scattering experiments in the energy region >9 meV. The relationship between the present results and the data reported so far is discussed to resolve the outstanding controversy regarding the phonon energies in solid p-H2. On the other hand, the excitation energies for solid o-D2 are in fairly good agreement with those of the neutron experiments. The calculated isothermal compressibility of solid p-H2 is found to be very close to the experimental result.
NASA Astrophysics Data System (ADS)
Pérez, Alejandro; Tuckerman, Mark E.; Müser, Martin H.
2009-05-01
The problems of ergodicity and internal consistency in the centroid and ring-polymer molecular dynamics methods are addressed in the context of a comparative study of the two methods. Enhanced sampling in ring-polymer molecular dynamics (RPMD) is achieved by first performing an equilibrium path integral calculation and then launching RPMD trajectories from selected, stochastically independent equilibrium configurations. It is shown that this approach converges more rapidly than periodic resampling of velocities from a single long RPMD run. Dynamical quantities obtained from RPMD and centroid molecular dynamics (CMD) are compared to exact results for a variety of model systems. Fully converged results for correlations functions are presented for several one dimensional systems and para-hydrogen near its triple point using an improved sampling technique. Our results indicate that CMD shows very similar performance to RPMD. The quality of each method is further assessed via a new χ2 descriptor constructed by transforming approximate real-time correlation functions from CMD and RPMD trajectories to imaginary time and comparing these to numerically exact imaginary time correlation functions. For para-hydrogen near its triple point, it is found that adiabatic CMD and RPMD both have similar χ2 error.
NASA Astrophysics Data System (ADS)
Kinugawa, Kenichi; Nagao, Hidemi; Ohta, Koji
2001-01-01
We present a formalism of the path integral centroid molecular dynamics (CMD) extended to Bose and Fermi statistics as a semiclassical approach to explore the dynamics of quantum many-body systems. The validity of the method is examined in relation to the time correlation functions. The presently proposed scheme, refined from our previous derivation [Chem. Phys. Lett. 307, 187 (1999)], is aimed at the calculations of not the exact quantum-mechanical dynamics but the semiclassical dynamics under certain approximations. The formalism is based on the projection operator with which the Bose/Fermi system is mapped onto a particular type of pseudo-Boltzmann system. In the pseudo-Boltzmann system the correlation due to the Bose/Fermi statistics is introduced via an extra pseudopotential called the permutation potential and its relevant operator. Using the present semiclassical formalism, the time correlation function of centroid position, which is evaluated from the CMD trajectories in the pseudo-Boltzmann system, is an approximation to the Kubo canonical correlation function of position operator of the exact quantum-statistical system composed of bosons or fermions. There is no such apparent relation between the momentum operator and the corresponding momentum centroid.
Azuri, Asaf; Engel, Hamutal; Doron, Dvir; Major, Dan Thomas
2011-05-10
A practical approach to treat nuclear quantum mechanical (QM) effects in simulations of condensed phases, such as enzymes, is via Feynman path integral (PI) formulations. Typically, the standard primitive approximation (PA) is employed in enzymatic PI simulations. Nonetheless, these PI simulations are computationally demanding due to the large number of discretizations, or beads, required to obtain converged results. The efficiency of PI simulations may be greatly improved if higher order factorizations of the density matrix operator are employed. Herein, we compare the results of model calculations obtained employing the standard PA, the improved operator of Takahashi and Imada (TI), and several gradient-based forward corrector algorithms due to Chin (CH). The quantum partition function is computed for the harmonic oscillator, Morse, symmetric, and asymmetric double well potentials. These potentials are simple models for nuclear quantum effects, such as zero-point energy and tunneling. It is shown that a unique set of CH parameters may be employed for a variety of systems. Additionally, the nuclear QM effects of a water molecule, treated with density functional theory, are computed. Finally, we derive a practical perturbation expression for efficient computation of isotope effects in chemical systems using the staging algorithm. This new isotope effect approach is tested in conjunction with the PA, TI, and CH methods to compute the equilibrium isotope effect in the Schiff base-oxyanion keto-enol tautomerism in the cofactor pyridoxal-5'-phosphate in the enzyme alanine racemase. The study of the different factorization methods reveals that the higher-order actions converge substantially faster than the PA approach, at a moderate computational cost.
NASA Astrophysics Data System (ADS)
He, Lianyi
2016-10-01
We present a standard field theoretical derivation of the dynamic density and spin linear response functions of a dilute superfluid Fermi gas in the BCS-BEC crossover in both three and two dimensions. The derivation of the response functions is based on the elegant functional path integral approach which allows us to calculate the density-density and spin-spin correlation functions by introducing the external sources for the density and the spin density. Since the generating functional cannot be evaluated exactly, we consider two gapless approximations which ensure a gapless collective mode (Goldstone mode) in the superfluid state: the BCS-Leggett mean-field theory and the Gaussian-pair-fluctuation (GPF) theory. In the mean-field theory, our results of the response functions agree with the known results from the random phase approximation. We further consider the pair fluctuation effects and establish a theoretical framework for the dynamic responses within the GPF theory. We show that the GPF response theory naturally recovers three kinds of famous diagrammatic contributions: the Self-Energy contribution, the Aslamazov-Lakin contribution, and the Maki-Thompson contribution. We also show that unlike the equilibrium state, in evaluating the response functions, the linear (first-order) terms in the external sources as well as the induced order parameter perturbations should be treated carefully. In the superfluid state, there is an additional order parameter contribution which ensures that in the static and long wavelength limit, the density response function recovers the result of the compressibility (compressibility sum rule). We expect that the f-sum rule is manifested by the full number equation which includes the contribution from the Gaussian pair fluctuations. The dynamic density and spin response functions in the normal phase (above the superfluid critical temperature) are also derived within the Nozières-Schmitt-Rink (NSR) theory.
Refaat, Tamer F; Singh, Upendra N; Petros, Mulugeta; Remus, Ruben; Yu, Jirong
2015-08-20
Double-pulsed 2-μm integrated path differential absorption (IPDA) lidar is well suited for atmospheric CO_{2} remote sensing. The IPDA lidar technique relies on wavelength differentiation between strong and weak absorbing features of the gas normalized to the transmitted energy. In the double-pulse case, each shot of the transmitter produces two successive laser pulses separated by a short interval. Calibration of the transmitted pulse energies is required for accurate CO_{2} measurement. Design and calibration of a 2-μm double-pulse laser energy monitor is presented. The design is based on an InGaAs pin quantum detector. A high-speed photoelectromagnetic quantum detector was used for laser-pulse profile verification. Both quantum detectors were calibrated using a reference pyroelectric thermal detector. Calibration included comparing the three detection technologies in the single-pulsed mode, then comparing the quantum detectors in the double-pulsed mode. In addition, a self-calibration feature of the 2-μm IPDA lidar is presented. This feature allows one to monitor the transmitted laser energy, through residual scattering, with a single detection channel. This reduces the CO_{2} measurement uncertainty. IPDA lidar ground validation for CO_{2} measurement is presented for both calibrated energy monitor and self-calibration options. The calibrated energy monitor resulted in a lower CO_{2} measurement bias, while self-calibration resulted in a better CO_{2} temporal profiling when compared to the in situ sensor.
Engel, Hamutal; Doron, Dvir; Kohen, Amnon; Major, Dan Thomas
2012-04-10
The inclusion of nuclear quantum effects such as zero-point energy and tunneling is of great importance in studying condensed phase chemical reactions involving the transfer of protons, hydrogen atoms, and hydride ions. In the current work, we derive an efficient quantum simulation approach for the computation of the momentum distribution in condensed phase chemical reactions. The method is based on a quantum-classical approach wherein quantum and classical simulations are performed separately. The classical simulations use standard sampling techniques, whereas the quantum simulations employ an open polymer chain path integral formulation which is computed using an efficient Monte Carlo staging algorithm. The approach is validated by applying it to a one-dimensional harmonic oscillator and symmetric double-well potential. Subsequently, the method is applied to the dihydrofolate reductase (DHFR) catalyzed reduction of 7,8-dihydrofolate by nicotinamide adenine dinucleotide phosphate hydride (NADPH) to yield S-5,6,7,8-tetrahydrofolate and NADP(+). The key chemical step in the catalytic cycle of DHFR involves a stereospecific hydride transfer. In order to estimate the amount of quantum delocalization, we compute the position and momentum distributions for the transferring hydride ion in the reactant state (RS) and transition state (TS) using a recently developed hybrid semiempirical quantum mechanics-molecular mechanics potential energy surface. Additionally, we examine the effect of compression of the donor-acceptor distance (DAD) in the TS on the momentum distribution. The present results suggest differential quantum delocalization in the RS and TS, as well as reduced tunneling upon DAD compression.
NASA Astrophysics Data System (ADS)
Durlak, Piotr; Latajka, Zdzisław
2009-10-01
Theoretical studies of the structure and proton motion in the intramolecular N-H⋯N hydrogen bond in 6-nitro-2,3-dipyrrol-2-ylquinoxaline anion were carried out at the DFT, MP2 and molecular dynamics levels. Geometry optimization at the 6-311++G(2d,2p) level demonstrate existence of two tautomers on the potential energy surface. The difference in energy between both tautomers is equals 1.62 (1.42) kcal/mol. Dynamics of proton motion in the N-H⋯N hydrogen bond was investigated in vacuum at 233 K using Car-Parrinello and path integral molecular dynamics. Very large delocalization of bridging proton is noted especially in path integral simulation. DFT calculated the coupling constant across the hydrogen bond equals 16.5 Hz is in good agreement with experimental value.
Nonadiabatic transition path sampling
NASA Astrophysics Data System (ADS)
Sherman, M. C.; Corcelli, S. A.
2016-07-01
Fewest-switches surface hopping (FSSH) is combined with transition path sampling (TPS) to produce a new method called nonadiabatic path sampling (NAPS). The NAPS method is validated on a model electron transfer system coupled to a Langevin bath. Numerically exact rate constants are computed using the reactive flux (RF) method over a broad range of solvent frictions that span from the energy diffusion (low friction) regime to the spatial diffusion (high friction) regime. The NAPS method is shown to quantitatively reproduce the RF benchmark rate constants over the full range of solvent friction. Integrating FSSH within the TPS framework expands the applicability of both approaches and creates a new method that will be helpful in determining detailed mechanisms for nonadiabatic reactions in the condensed-phase.
Lindoy, Lachlan P.; Kolmann, Stephen J.; D’Arcy, Jordan H.; Jordan, Meredith J. T.; Crittenden, Deborah L.
2015-11-21
Finite temperature quantum and anharmonic effects are studied in H{sub 2}–Li{sup +}-benzene, a model hydrogen storage material, using path integral Monte Carlo (PIMC) simulations on an interpolated potential energy surface refined over the eight intermolecular degrees of freedom based upon M05-2X/6-311+G(2df,p) density functional theory calculations. Rigid-body PIMC simulations are performed at temperatures ranging from 77 K to 150 K, producing both quantum and classical probability density histograms describing the adsorbed H{sub 2}. Quantum effects broaden the histograms with respect to their classical analogues and increase the expectation values of the radial and angular polar coordinates describing the location of the center-of-mass of the H{sub 2} molecule. The rigid-body PIMC simulations also provide estimates of the change in internal energy, ΔU{sub ads}, and enthalpy, ΔH{sub ads}, for H{sub 2} adsorption onto Li{sup +}-benzene, as a function of temperature. These estimates indicate that quantum effects are important even at room temperature and classical results should be interpreted with caution. Our results also show that anharmonicity is more important in the calculation of U and H than coupling—coupling between the intermolecular degrees of freedom becomes less important as temperature increases whereas anharmonicity becomes more important. The most anharmonic motions in H{sub 2}–Li{sup +}-benzene are the “helicopter” and “ferris wheel” H{sub 2} rotations. Treating these motions as one-dimensional free and hindered rotors, respectively, provides simple corrections to standard harmonic oscillator, rigid rotor thermochemical expressions for internal energy and enthalpy that encapsulate the majority of the anharmonicity. At 150 K, our best rigid-body PIMC estimates for ΔU{sub ads} and ΔH{sub ads} are −13.3 ± 0.1 and −14.5 ± 0.1 kJ mol{sup −1}, respectively.
NASA Astrophysics Data System (ADS)
Smith, Eric A.; Turk, F. Joseph; Farrar, Michael R.; Mugnai, Alberto; Xiang, Xuwu
1997-04-01
This study presents research in support of the design and implementation of a combined radar-radiometer algorithm to be used for precipitation retrieval during the Tropical Rainfall Measuring Mission (TRMM). The combined algorithm approach is expected to overcome various difficulties that arise with a radar-only approach, particularly related to estimates of path-integrated attenuation (PIA) along the TRMM radar beam. A technique is described for estimating PIA at the 13.8-GHz frequency of the TRMM precipitation radar (PR) from 10.7-GHz brightness temperature TB measurements obtained from the TRMM microwave imager. Because the PR measures at an attenuating frequency, an independent estimate of PIA is used to constrain the solution to the radar equation, which incorporates effects of attenuation propagation along a radar beam. Through the use of variational or probabilistic techniques, the independent PIA calculations provide a means to adjust for errors that accumulate in estimates of range-dependent rain rates at progressively increasing range positions from radar reflectivity vectors. The accepted radar approach for obtaining PIA from ocean-viewing radar reflectivity measurements is called the surface reference technique, a scheme based on the difference in ocean surface cross sections between cloud-free and raining radar pixels. This technique has encountered problems, which are discussed and analyzed with the aid of coordinated aircraft radar (Airborne Rain Mapping Radar) and radiometer (Advanced Microwave Precipitation Radiometer) measurements obtained during the west Pacific Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment in 1993. The derived relationship expressing 13.8-GHz PIAs as a function of 10.7-GHz TB's is based on statistical fitting of many thousands of radiative transfer (RTE) calculations in which the relevant physical and radiative parameters affecting transmission, absorption, and scattering in a raining column and
NASA Technical Reports Server (NTRS)
Ward, Charles; Bravo, Jessica; De Luna, Rosalia; Lopez, Gerardo; Pichardo, Itza; Trejo, Danny; Vargas, Gabriel
1997-01-01
One of the research groups at the Pan American Center for Earth and Environmental Studies (PACES) is researching the northward migration path of Africanized Honey Bees or often referred to in the popular press as killer bees. The goal of the Killer Bee Research Group (KBRG) is to set up a database in the form of a geographical information system, which will be used to track and predict the bees future migration path. Included in this paper is background information on geographical information systems, the SPANS Explorer software package which was used to implement the database, and Advanced Very High Resolution Radiometer data and how each of these is being incorporated in the research. With an accurate means of predicting future migration paths, the negative effects of the Africanized honey bees maybe reduced.
ERIC Educational Resources Information Center
Malgieri, Massimiliano; Onorato, Pasquale; De Ambrosis, Anna
2017-01-01
In this paper we present the results of a research-based teaching-learning sequence on introductory quantum physics based on Feynman's sum over paths approach in the Italian high school. Our study focuses on students' understanding of two founding ideas of quantum physics, wave particle duality and the uncertainty principle. In view of recent…
Career Paths in Environmental Sciences
Career paths, current and future, in the environmental sciences will be discussed, based on experiences and observations during the author's 40 + years in the field. An emphasis will be placed on the need for integrated, transdisciplinary systems thinking approaches toward achie...
Employer Resource Manual. Project Path.
ERIC Educational Resources Information Center
Kane, Karen R.; Del George, Eve
Project Path at Illinois' College of DuPage was established to provide pre-employment training and career counseling for disabled students. To encourage the integration of qualified individuals with disabilities into the workplace, the project compiled this resource manual for area businesses, providing tips for interacting with disabled people…
NASA Technical Reports Server (NTRS)
Singh, Upendra N.; Petros, Mulugeta; Refaat, Tamer F.; Yu, Jirong; Antill, Charles W.; Remus, Ruben
2016-01-01
This presentation will provide status and details of an airborne 2-micron triple-pulse integrated path differential absorption (IPDA) lidar being developed at NASA Langley Research Center with support from NASA ESTO Instrument Incubator Program. The development of this active optical remote sensing IPDA instrument is targeted for measuring both atmospheric carbon dioxide and water vapor in the atmosphere from an airborne platform. This presentation will focus on the advancement of the 2-micron triple-pulse IPDA lidar development. Updates on the state-of-the-art triple-pulse laser transmitter will be presented including the status of seed laser locking, wavelength control, receiver and detector upgrades, laser packaging and lidar integration. Future plan for IPDA lidar system for ground integration, testing and flight validation will also be presented.
A Note on the Stochastic Nature of Feynman Quantum Paths
NASA Astrophysics Data System (ADS)
Botelho, Luiz C. L.
2016-11-01
We propose a Fresnel stochastic white noise framework to analyze the stochastic nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under a time-independent potential.
NASA Astrophysics Data System (ADS)
Vogelbacher, Silke; van Eijk, Alexander M. J.; Sprung, Detlev; Cohen, Leo H.; Sucher, Erik; Stein, Karin
2016-10-01
A transmission experiment has been performed over an optical path of 1.53 km at a rural test site in Meppen, Northwest Germany. Direct transmission measurements were made by a 7-wavelength transmissometer. Transmission was further estimated from the average voltage received by a BLS2000 scintillometer, and evaluated with Mie theory from in-situ aerosol measurements near the optical path. Furthermore, the transmission was modeled with MODTRAN, driven with local meteorology, visibility and the rural aerosol model. For a central wavelength of 0.88μm, the transmissometer, the BLS200 and MODTRAN agree well. Remaining differences may be due to water transmission and continuum around 0.95μm that is picked up by the transmissometer and not by the narrow-banded BLS2000 and MODTRAN calculations. When MODTRAN is run without an aerosol model, or when this model is driven by a "default" visibility, the overlap with the measurements is extremely poor.
Adaptively Ubiquitous Learning in Campus Math Path
ERIC Educational Resources Information Center
Shih, Shu-Chuan; Kuo, Bor-Chen; Liu, Yu-Lung
2012-01-01
The purposes of this study are to develop and evaluate the instructional model and learning system which integrate ubiquitous learning, computerized adaptive diagnostic testing system and campus math path learning. The researcher first creates a ubiquitous learning environment which is called "adaptive U-learning math path system". This…
NASA Astrophysics Data System (ADS)
Militzer, Burkhard
2003-06-01
Path integral Monte Carlo simulations have been used to study deuterium at high pressure and temperature. The equation of state has been derived in the temperature and density regions of 10 000 leq T leq 1 000 000 K and 0.6 leq rho leq 2.5 g cm-3. A series of shock Hugoniot curves is computed for different initial compressions in order to compare with current and future shock wave experiments using liquid deuterium samples precompressed in diamond anvil cells. Submitted to Proceedings of the Conference on Strongly Coupled Coulomb Systems 2002 in Santa Fe.
Zhao, Yi; Yamamoto, Takeshi; Miller, William H
2004-02-15
The quantum instanton approximation for thermal rate constants of chemical reactions [Miller, Zhao, Ceotto, and Yang, J. Chem. Phys. 119, 1329 (2003)], which is modeled after the earlier semiclassical instanton approach, is applied to the hydrogen abstraction reaction from methane by a hydrogen atom, H + CH4 --> H2 + CH3, using a modified and recalibrated version of the Jordan-Gilbert potential surface. The quantum instanton rate is evaluated using path integral Monte Carlo approaches based on the recently proposed implementation schemes [Yamamoto and Miller, J. Chem. Phys. 120, 3086 (2004)]. The calculations were carried out using the Cartesian coordinates of all the atoms (thus involving 18 degrees of freedom), thereby taking explicit account of rotational effects of the whole system and also allowing the equivalent treatment of the four methane hydrogens. To achieve such a treatment, we present extended forms of the path integral estimators for relevant quantities that may be used for general N-atom systems with any generalized reaction coordinates. The quantum instanton rates thus obtained for the temperature range T = 200-2000 K show good agreement with available experimental data, which gives support to the accuracy of the underlying potential surface used.
ERIC Educational Resources Information Center
Yu, Baohua
2013-01-01
This study examined the interrelationships of integrative motivation, competence in second language (L2) communication, sociocultural adaptation, academic adaptation and persistence of international students at an Australian university. Structural equation modelling demonstrated that the integrative motivation of international students has a…
Moody, A.
2012-05-11
The ap command traveres all symlinks in a given file, directory, or executable name to identify the final absolute path. It can print just the final path, each intermediate link along with the symlink chan, and the permissions and ownership of each directory component in the final path. It has functionality similar to "which", except that it shows the final path instead of the first path. It is also similar to "pwd", but it can provide the absolute path to a relative directory from the current working directory.
NASA Astrophysics Data System (ADS)
Blake, J. I.; Jackson, C. R.; Griffiths, N. A.; Klaus, J.; Du, E.; Vache, K. B.; McDonnell, J. J.
2012-12-01
Best Management Practices designed to protect water quality are largely based on empirical studies of runoff from various cropping practices and associated mitigation strategies. Application of the resulting mitigation strategies has resulted in significant improvements in water quality, particularly reductions in sediment yields. Watershed modeling can extend the observations to other crops, landscapes and climates, but extrapolation is often compromised by too many model parameters and assumptions. The sheer number of potential dedicated biofuel-biochemical crop species, crop practices and hydrologic landscapes makes it difficult to comprehensively test various alternatives when the final configurations are largely unknown. We argue that a dominant hydrologic process framework for evaluating and mitigating potential water quality impacts can be constructed from basic hydrologic principles coupled to the crop fertilizer uptake efficiency and pesticide properties. We illustrate the approach in the southeastern U.S. on an old-field landscape with zero and first order streams suitable for cellulosic biofuel crops. In this region nitrogen additions are essential to sustain and enhance production and herbicides are frequently required for establishment. If overland flow is effectively managed, the primary flow path transmits water to groundwater and contaminates are subject to dispersion, sorption, and biochemical reaction. Average residence times in headwater basins typically ranges from3-12 years. However, the array of flow paths and distribution of residence times may lead to undesirable transport of contaminates. For example, significant lateral interflow may occur within 25-50 meters of the stream interface. Transmissions of these materials through the biological active riparian zones can substantially reduce contaminate concentrations as long as flux rates do not exceed uptake rates. To the extent that subsurface interflow and groundwater dynamics can be
ERIC Educational Resources Information Center
Stimpfel, Scott Albert
2013-01-01
Nearly half of all undergraduates in the U.S. are enrolled in community colleges and many aspire to obtain a baccalaureate degree, however, less than 13% do so within six years. Integration has been identified in higher education literature as a salient factor contributing to students' persistence. Empirical evidence suggests that…
Whishaw, I Q; Gorny, B
1999-06-01
Allothetic and idiothetic navigation strategies use very different cue constellations and computational processes. Allothetic navigation requires the use of the relationships between relatively stable external (visual, olfactory, auditory) cues, whereas idiothetic navigation requires the integration of cues generated by self-movement and/or efferent copy of movement commands. The flexibility with which animals can switch between these strategies and the neural structures that support these strategies are not well understood. By capitalizing on the proclivity of foraging rats to carry large food pellets back to a refuge for eating, the present study examined the contribution of the hippocampus to the use of allothetic versus idiothetic navigation strategies. Control rats and fimbria-fornix-ablated rats were trained to follow linear, polygonal, and octagonal scent trails that led to a piece of food. The ability of the rats to return to the refuge with the food via the shortest route using allothetic cues (visual cues and/or the odor trail available) or using ideothetic cues (the odor trail removed and the rats blindfolded or tested in infrared light) was examined. Control rats "closed the polygon" by returning directly home in all cue conditions. Fimbria-fornix rats successfully used allothetic cues (closed the polygon using visual cues or tracked back on the string) but were insensitive to the direction and distance of the refuge and were lost when restricted to idiothetic cues. The results support the hypothesis that the hippocampal formation is necessary for navigation requiring the integration of idiothetic cues.
NASA Astrophysics Data System (ADS)
Janse van Rensburg, E. J.
2010-08-01
In this paper the models of pulled Dyck paths in Janse van Rensburg (2010 J. Phys. A: Math. Theor. 43 215001) are generalized to pulled Motzkin path models. The generating functions of pulled Motzkin paths are determined in terms of series over trinomial coefficients and the elastic response of a Motzkin path pulled at its endpoint (see Orlandini and Whittington (2004 J. Phys. A: Math. Gen. 37 5305-14)) is shown to be R(f) = 0 for forces pushing the endpoint toward the adsorbing line and R(f) = f(1 + 2cosh f))/(2sinh f) → f as f → ∞, for forces pulling the path away from the X-axis. In addition, the elastic response of a Motzkin path pulled at its midpoint is shown to be R(f) = 0 for forces pushing the midpoint toward the adsorbing line and R(f) = f(1 + 2cosh (f/2))/sinh (f/2) → 2f as f → ∞, for forces pulling the path away from the X-axis. Formal combinatorial identities arising from pulled Motzkin path models are also presented. These identities are the generalization of combinatorial identities obtained in directed paths models to their natural trinomial counterparts.
1985-11-01
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Denholm, Paul; Clark, Kara; O'Connell, Matt
2016-05-01
This report examines how the bulk power system may need to evolve to accommodate the increased photovoltaic (PV) penetration resulting from achievement of the U.S. Department of Energy's SunShot cost targets. The variable and uncertain nature of PV-generated electricity presents grid-integration challenges. For example, the changing net load associated with high midday PV generation and low electricity demand can create 'overgeneration' that requires curtailment of PV output and reduces PV's value and cost-competitiveness. Accommodating the changes in net load resulting from increased variable generation requires enhancements to a power system's 'flexibility,' or ability to balance supply and demand over multiple time scales through options including changes in system operation, flexible generation, reserves from solar, demand response, energy storage, and enhanced transmission and regional coordination. For utility-scale PV with a baseline SunShot levelized cost of electricity (LCOE) of 6 cents/kWh, increasing the annual energy demand met by solar energy from 10% to 20% would increase the marginal LCOE of PV from 6 cents/kWh to almost 11 cents/kWh in a California grid system with limited flexibility. However, increasing system flexibility could minimize solar curtailment and keep PV cost-competitive at penetrations at least as high as 25%. In the longer term, energy storage technologies--such as concentrating solar power with thermal energy storage--could facilitate the cost-effective integration of even higher PV penetration. Efficient deployment of the grid-flexibility options needed to maintain solar's value will require various innovations, from the development of communication, control, and energy storage technologies to the implementation of new market rules and operating procedures.
Johnson, B.M.; Mellinger, G.; Strachan, D.; Hallen, R.
1991-09-01
The watch list'' waste tanks at the Hanford Site in Washington state are those that the Secretary of the Department of Energy reports upon to the Congress because of the unresolved safety question. As such, they are subject to intense surveillance and an enhanced list of controls and safety procedures. The objective of the Waste Tank Safety Program is to mitigate the safety concerns with respect to these tanks, thereby removing them from the watch list.'' The essential step in this process is the development of a defensible position that reduce the risk of these tanks to an acceptable level. An integrated research and development (R D) program is believed to be the most cost-effective means of achieving the information required to mitigate the safety concern and to resolve the safety issues. This program uses chemical and physical modeling studies of synthetic waste, is substantiated with limited field data and radioactive samples from a tank, and uses numerical modeling to extrapolate results to actual tank-scale operations. 3 refs., 4 figs.
Denholm, Paul; Clark, Kara; O'Connell, Matt
2016-05-01
Increasing the use of grid-flexibility options (improved grid management, demand response, and energy storage) could enable 25% or higher penetration of PV at low costs (see Denholm et al. 2016). Considering the large-scale integration of solar into electric-power systems complicates the calculation of the value of solar. In fact a comprehensive examination reveals that the value of solar technologies—or any other power-system technology or operating strategy—can only be understood in the context of the generation system as a whole. This is well illustrated by analysis of curtailment at high PV penetrations within the bulk power and transmission systems. As the deployment of PV increases, it is possible that during some sunny midday periods due to limited flexibility of conventional generators, system operators would need to reduce (curtail) PV output in order to maintain the crucial balance between electric supply and demand. As a result, PV’s value and cost competitiveness would degrade. For example, for utility-scale PV with a baseline SunShot LCOE of 6¢/kWh, increasing the annual energy demand met by solar energy from 10% to 20% would increase the marginal LCOE of PV from 6¢/kWh to almost 11¢/kWh in a California grid system with limited flexibility. However, this loss of value could be stemmed by increasing system flexibility via enhanced control of variable-generation resources, added energy storage, and the ability to motivate more electricity consumers to shift consumption to lower-demand periods. The combination of these measures would minimize solar curtailment and keep PV cost-competitive at penetrations at least as high as 25%. Efficient deployment of the grid-flexibility options needed to maintain solar’s value will require various innovations, from the development of communication, control, and energy storage technologies to the implementation of new market rules and operating procedures.
NASA Astrophysics Data System (ADS)
Karakullukcu, Baris; Kanick, Stephen; Aans, Jan Bonne; Sterenborg, Henricus; Tan, Bing; Amelink, Arjen; Robinson, Dominic
2015-04-01
The use of fluorescence differential pathlength spectroscopy (FDPS) has the potential to provide real-time information on photosensitiser pharmacokinetics, vascular physiology and photosensitizer photobleaching based dosimetry of tumors in the oral cavity receiving m-tetrahydroxyphenylchlorin (mTHPC) photodynamic therapy (PDT). Reflectance spectra can be used provide quantitative values of oxygen saturation, blood volume fraction, blood vessel diameter, and to determine the local optical properties that can be used to correct raw fluorescence for tissue absorption. Patients and methods: Twenty-seven lesions in the oral cavity, either dysplasias or cancer were interrogated using FDPS, before and immediately after the therapeutic illumination. The average tumor center to normal mucosa ratio of fluorescence was 1.50 ± 0.66. mTHPC photobleaching was observed in 24 of the lesions treated. The average extent of photobleaching was 81% ± 17%. Information from FDPS spectroscopy coupled with the clinical results of the treatment identified 3 types of correctable errors in the application of mTHPC-PDT: Two patients exhibited very low concentrations of photosensitizer in tumour center, indicating an ineffective i.v. injection of photosensitiser or an erroneous systemic distribution of mTHPC. In one in tumor we observed no photobleaching accompanied by a high blood volume fraction in the illuminated tissue, suggesting that the presence of blood prevented therapeutic light reaching the target tissue. All 3 of the these lesions had no clinical response to PDT. In four patients we observed less than 50% photobleaching at the tumor margins , suggesting a possible geographic miss. One patient in this group had a recurrence within 2 months after PDT even though the initial response was good. The integration of FDPS to clinical PDT yields data on tissue physiology, photosensitiser content and photobleaching that can help identify treatment errors that can potentially be corrected.
ERIC Educational Resources Information Center
Kalyn, Brenda
2006-01-01
Integrated learning is an exciting adventure for both teachers and students. It is not uncommon to observe the integration of academic subjects such as math, science, and language arts. However, educators need to recognize that movement experiences in physical education also can be linked to academic curricula and, may even lead the…
Nonholonomic catheter path reconstruction using electromagnetic tracking
NASA Astrophysics Data System (ADS)
Lugez, Elodie; Sadjadi, Hossein; Akl, Selim G.; Fichtinger, Gabor
2015-03-01
Catheter path reconstruction is a necessary step in many clinical procedures, such as cardiovascular interventions and high-dose-rate brachytherapy. To overcome limitations of standard imaging modalities, electromagnetic tracking has been employed to reconstruct catheter paths. However, tracking errors pose a challenge in accurate path reconstructions. We address this challenge by means of a filtering technique incorporating the electromagnetic measurements with the nonholonomic motion constraints of the sensor inside a catheter. The nonholonomic motion model of the sensor within the catheter and the electromagnetic measurement data were integrated using an extended Kalman filter. The performance of our proposed approach was experimentally evaluated using the Ascension's 3D Guidance trakStar electromagnetic tracker. Sensor measurements were recorded during insertions of an electromagnetic sensor (model 55) along ten predefined ground truth paths. Our method was implemented in MATLAB and applied to the measurement data. Our reconstruction results were compared to raw measurements as well as filtered measurements provided by the manufacturer. The mean of the root-mean-square (RMS) errors along the ten paths was 3.7 mm for the raw measurements, and 3.3 mm with manufacturer's filters. Our approach effectively reduced the mean RMS error to 2.7 mm. Compared to other filtering methods, our approach successfully improved the path reconstruction accuracy by exploiting the sensor's nonholonomic motion constraints in its formulation. Our approach seems promising for a variety of clinical procedures involving reconstruction of a catheter path.
Accelerating cleanup: Paths to closure
Edwards, C.
1998-06-30
This document was previously referred to as the Draft 2006 Plan. As part of the DOE`s national strategy, the Richland Operations Office`s Paths to Closure summarizes an integrated path forward for environmental cleanup at the Hanford Site. The Hanford Site underwent a concerted effort between 1994 and 1996 to accelerate the cleanup of the Site. These efforts are reflected in the current Site Baseline. This document describes the current Site Baseline and suggests strategies for further improvements in scope, schedule and cost. The Environmental Management program decided to change the name of the draft strategy and the document describing it in response to a series of stakeholder concerns, including the practicality of achieving widespread cleanup by 2006. Also, EM was concerned that calling the document a plan could be misconstrued to be a proposal by DOE or a decision-making document. The change in name, however, does not diminish the 2006 vision. To that end, Paths to Closure retains a focus on 2006, which serves as a point in time around which objectives and goals are established.
Path planning under spatial uncertainty.
Wiener, Jan M; Lafon, Matthieu; Berthoz, Alain
2008-04-01
In this article, we present experiments studying path planning under spatial uncertainties. In the main experiment, the participants' task was to navigate the shortest possible path to find an object hidden in one of four places and to bring it to the final destination. The probability of finding the object (probability matrix) was different for each of the four places and varied between conditions. Givensuch uncertainties about the object's location, planning a single path is not sufficient. Participants had to generate multiple consecutive plans (metaplans)--for example: If the object is found in A, proceed to the destination; if the object is not found, proceed to B; and so on. The optimal solution depends on the specific probability matrix. In each condition, participants learned a different probability matrix and were then asked to report the optimal metaplan. Results demonstrate effective integration of the probabilistic information about the object's location during planning. We present a hierarchical planning scheme that could account for participants' behavior, as well as for systematic errors and differences between conditions.
Path planning strategies for autonomous ground vehicles
NASA Astrophysics Data System (ADS)
Gifford, Kevin Kent
hierarchical software control architecture is introduced that uses as the main guidance function an arbitration-based scheme which is able to efficiently and robustly integrate disparate sensor data. The flexibility provided by such an architecture allows for very easy integration of any type of environmental sensing device into the path planning algorithm.